MAS291

An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. What is the population?

all custormers

A basketball player has made 70% of his foul shots during the season. If he shoots 3 foul shots in tonight's game, what is the probability that he makes all of the shots?

b. 0.343

Find z if the normal curve area to the left of z is 0.1611.

-0.99

Assume that a procedure yields a binomial distribution with a trial repeated 4 times. Use the binomial probability formula to find the probability of 3 successes given the probability 1/6 of success on a single trial.

0.0154

Let X be a random variable has the following uniform density function f(x) = 0.1 when 0< x < 10. What is the probability that the random variable X has a value greater than 5.3?

0.47

A percentage distribution is given below for the size of families in one U.S. city. Size

0.950

The height y and base diameter x of five trees of a certain variety produced the following data. Compute the correlation coefficient r.

0.98

A telemarketer found that there was a 1% chance of a sale from his phone solicitations. Find the probability of getting 5 or more sales for 1000 telephone calls.

b. 0.9599

(See picture) [file:2258.jpg]

9.209

(See picture)

(186.3, 197.7)

(See picture) [file:1968.jpg]

(i)

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(Z > c) = 0.1093, find c.

1.23

If P(A) = 0.72, P(B) = 0.11, and A and B are independent, find P(A

B). | 0.72

In hypothesis testing, the null hypothesis should contain the equality sign.

True

The FPT university claims that 20% of its graduates are women. In a graduating class of 250 students, 60 were women. At = 0.05, does this suggest that the school is believable? Let z0.025 = 1.96 and z0.05 = 1.65.

Yes, because |z0| = 1.58 < z0.025

(4335) (11081) [file:2182.jpg]

[765, 795]

Which of the following represents the strongest linear correlation?

a. -0.97

Flip a coin twice, create the sample space of possible outcomes.

a. HH HT TH TT

The width of a confidence interval estimate for a proportion will be

narrower for 90% confidence than for 99% confidence.

The residuals represent

the difference between the actual Y values and the predicted Y values.

The test scores of 32 students are listed below. Find Q3. 32 37 41 44 46 48 53 55 56 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 80 82 83 86 89 92 95 99

79.5

The cumulative distribution function of a random variable X is given by What is the value of the probability density function at x = 1?

0.15

The probability of winning a certain lottery is 1/9999. For people who play 246 times, find the standard deviation for the random variable X, the number of wins.

0.1568

Find the test statistic t0 for a sample with n = 27, = 21, s = 3.3, and α = 0.005 if H1: μ > 20. Round your answer to three decimal places.

1.575

Find the mean for the binomial distribution which has the stated values of n = 20 and p = 3/5. Round answer to the nearest tenth.

12.0

According to a college survey, 12% of all students work full time. Find the mean for the number of students who work full time in samples of size 54.

6.48

(See picture) [file:1986.jpg]

8

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 420 hours and a standard deviation of 15 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations of the mean?

95%

The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the variance for the probability distribution.

a. 0.59

Assume that the heights of men are normally distributed. A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of 3.2 inches. Construct a 99% confidence interval for the population standard deviation, $$\sigma.$$

d. (2.2, 5.8)

Of 900 randomly selected cases of lung cancer, 360 resulted in death within five years. Construct a 95% two-sided confidence interval on the death rate from lung cancer.

(0.37, 0.43)

Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they watched television was 20.5 with a standard deviation of 4.6 hours.

(18.81, 22.19)

(See picture) [file:2212.jpg]

(186.3, 197.7)

Assume that the heights of men are normally distributed. A random sample of 19 men have a mean height of 65.5 inches and a standard deviation of 3.0 inches. Construct a 99% confidence interval for the population standard deviation,

(2.1, 5.1)

Assume that the heights of men are normally distributed. A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of 3.2 inches. Construct a 99% confidence interval for the population standard deviation, (sigma).

(2.2, 5.8)

A group of 49 randomly selected students has a mean age of 22.4 years with a population standard deviation of 3.8. Construct a 98% confidence interval for the population mean.

(21.1, 23.7)

A group of 49 randomly selected students has a mean age of 22.4 years with a population standard deviation of 3.8. Construct a 98% confidence interval for the population mean. [file:2194.jpg]

(21.1, 23.7)

A random sample of 40 students has a mean annual earnings of 3120 and a population standard deviation of 677. Construct the confidence interval for the population mean. Use a 95% confidence level.

(2910, 3330)

The probability of a successful optical alignment in the assembly of an optical data storage product is 0.8. Assume the trials are independent. What is the probability that the first successful alignment requires exactly four trials?

0.0064

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.5 pounds and standard deviation of 0.7 pound. If a sample of 64 fish is randomly selected, what is probability that the sample mean is more than 3.7 pounds?

0.0111

A multiple-choice quiz has 20 questions each with 4 possible answers of which only 1 is the correct answer. What is the probability that sheer guesswork yields 4 correct answers for 5 of the 20 problems about which the student has no knowledge?

0.0146

The average score of all golfers for a particular course has a mean of 80 and a standard deviation of 3. Suppose 100 golfers played the course today. Find the probability that the average score of the 100 golfers exceeded 80.5.

0.0478

For women aged 18-24, systolic blood pressures ( in mm Hg) are normally distributed with a mean of 115 and a standard deviation of 13. If 25 women aged 18-24 are randomly selected, find the probability that their mean systolic blood pressures is between 119 and 122.

0.0584

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 350 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 310 and 295.

0.0762

Suppose that and =15 for a population. In a sample where n = 100 is randomly taken, what is the variance for the sample mean?

0.15

Let the random variable X have a discrete uniform distribution on the integers 12, 13, ..., 19. Find the value of P(X > 17).

0.25

A normal distribution has mean μ = 60 and standard deviation σ = 6, find the area under the curve to the right of 64.

0.2525

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 5 minutes. What proportion of customers having to hold more than 6.5 minutes will hang up before placing an order?

0.27253

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 41 to 81. What is the probability that this experiment results in an outcome less than 56?

0.375

A group of volunteers for a clinical trial consists of 123 women and 178 men. 54 of the women and 46 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person is a man given that they have high blood pressure.

0.460

A population of Australian Koala bears has a mean height of 21 inches and a standard deviation of 4.5 inches. You plan to choose a sample of 64 bears at random. What is the probability of a sample mean between 21 and 22.

0.4623

You wish to test the claim that μ = 1200 at a level of significance of α = 0.01 andsample statistics are given n = 37, s =80, . Compute the value of the test statistic. Round your answer to two decimal places.

0.53

The volumes of soda in quart soda bottles are normally distributed with a mean of 22.3 oz and a standard deviation of 1.6 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 23.1 oz?

0.6915

Suppose X is a uniform random variable over the interval [40, 50]. Find the probability that a randomly selected observation exceeds 43.

0.7

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,500 miles and a standard deviation of 2800 miles. What is the probability a particular tire of this brand will last longer than 58,400 miles?

0.7734

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.07 for a test H1: µ0.

1.476

What is the standard deviation of the following probability distribution? x

1.54

How many baseball teams of nine members can be chosen from among twelve boys, without regard to the position played by each member?

220

The range of the random variable X is {1, 2, 3, 6, u}, where u is unknown. If each value is equally likely and the mean of X is 10, determine the value of u.

38

Find the mean for the binomial distribution which has the values of n = 33 and p = 0.2. Round answer to the nearest tenth.

6.6

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. Find the waiting time at which only 10% of the customers will continue to hold.

6.9 minutes

The scores for a statistics test are as follows: Compute the mean score.

73.90

Find the variance for the given sample data 53 52 75 62 68 58 49 49

89.6

(See picture) [file:2252.jpg]

Reject the null hypothesis

It is desired to estimate the average total compensation of CEOs. Data were randomly collected from 32 CEOs and the 95% confidence interval was calculated to be ($3 212 540, $6 020 240). Which of the following interpretations is correct?

We are 95% confident that the average total compensation of all CEOs falls in the interval $3 212 540 to $6 020 240.

Determine whether the given conditions justify testing a claim about a population mean μ. If so, what is formula for test statistic? The sample size is n = 17, σ is not known, and the original population is normally distributed.

Yes, test statistic =

For a sample of 45 observations, you have the following information: Σxi = 153.7, Σyi = 231.2, Σxiyi = 712.5, Σ(xi)2 = 718, Σ(yi)2 = 1775.2. What is the sample correlation coefficient between X and Y?

a. -0.23

Suppose that $$X$$ is a negative binomial random variable with $$p = 0.2$$ and $$r = 4$$. Determine $$P(X=20)$$.

a. 0.0436

If the coefficient of correlation is 0.78, what does the coefficient of determination equal?

a. 0.6084

The height y and base diameter x of five tree of a certain variety produced the following data x 2 2 3 5 y 30 40 90 100 Compute the correlation coefficient.

a. 0.873

A study of 1000 randomly selected flights of a major airline showed that 782 of the flights arrived on time. What is the probability of a flight arriving on time?

a. 391/500

Determine whether the given conditions justify testing a claim about a population mean μ. The sample size is n = 49, σ = 12.3, and the original population is not normally distributed.

a. Yes

For two events A and B, P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0. It follows that A and B are

b. disjoint but not independent.

Let X be a uniform random variable over the interval [1, 9] . What is the probability that the random variable X has a value less than 6?

c. 0.400

Suppose x is a uniform random variable over [10,90]. Find the probability that a randomly selected observation exceeds 26.

c. 0.8

Assume that we found out the regression equation = 1.6 +x corresponding to the data below x 0 1 2 4 5 y 1 2 4 5 7 Find the error sum of square SSE.

c. 0.919

If $$X$$ is uniformly distributed over the interval $$[0, 10]$$. Compute the probability that $$2 < X < 9$$.

c. 7/10

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 360 hours and a standard deviation of 8 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations of the mean?

d. 95%

Which of the following is a discrete quantitative variable?

d. The number of employees of an insurance company

Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. Test 1 7.5 6.4 6.6 5.8 8.3 Test 2 6.7 6.6 7.2 4.0 6.7 Find the value of the linear correlation coefficient r.

e. 0.58

When considering area under the standard normal curve, decide whether the area between z = -1.5 and z = 1.1 is bigger than, smaller than, or equal to the area between z = -1.1 and z = 1.5.

equal to

The peak shopping time at home improvement store is between 8-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 150 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that a sapmle of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store.

number of items - discrete; total time - continuous

The mean of a data set is 36.71, and the sample standard deviation s is 3.22. Find the interval representing measurements within one standard deviation of the mean.

(33.49, 39.93)

A random sample of 68 fluorescent light bulbs has a mean life of 600 hours with a population standard deviation of 25 hours. Construct a 95% confidence interval for the population mean.

(594.1, 605.9)

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 61,000 miles and a standard deviation of 2100 miles. What is the probability a certain tire of this brand will last between 60,010 miles and 58,580 miles?

0.1941

Let the random variable X have a discrete uniform distribution on the integers Determine P(X < 6).

0.5

The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the variance for the probability distribution.

0.69

A study of the checkout times of 100 customers at a supermarket resulted in the distribution below. Find the mean and standard deviation. x (minutes)

3.3 and 1.4599

The probability that a house in an urban area will be burglarized is 15%. If 30 houses are randomly selected, what is the mean of the number of houses burglarized?

4.5

The State Transportation Department is interested in estimating the proportion of vehicle owners that are operating vehicles without the required liability insurance. If they wish to estimate the population proportion within ± 0.08 and use 96 percent confidence, what is the largest random sample that they will need?

About 165

The owner of a football team claims that the average attendance at games is over 79,000, and he is therefore justified in moving the team to a city with a larger stadium. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

H0: μ, the average attendance at games, is equal to 79,000 H1: μ, the average attendance at games, is greater than 79,000

Flip a coin twice, create the sample space of possible outcomes (H: Head, T: Tail).

HH HT TH TT

It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be (2181260, 5836180). Which of the following interpretations is correct?

We are 97% confident that the average total compensation of all CEOs in the Service industry falls in the interval 2181260 to 5836180.

Find the value of the linear correlation coefficient r. x 85.3 78.3 80.6 95.8 y 12.2 15.1 19.4 17.4

a. 0.07

When considering area under the standard normal curve, decide whether the area between z = 3 andz = -3 is bigger than, smaller than, or equal to the area betweenz =2.7 and z = 2.9.

bigger than

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 90\% confidence interval to estimate the true proportion of students who receive financial aid. Let $$z_{0.1}=1.28;z_{0.05}=1.65$$.

c. (0.533; 0.647)

In one region, the September energy consumption levels for single-family homes are normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.

c. 0.1971

Find the mean of thefollowing probability distribution. x 0 1 2 3 4 P(x) 0.19 0.37 0.16 0.26 0.02

c. 1.55

Suppose a 95% confidence interval for μ turns out to be (1000, 2100). Give a definition of what it means to be "95% confident" in an inference.

c. In repeated sampling, 95% of the intervals constructed would contain the population mean.

Identify the choice that best completes the statement Given the least squares regression line = 12.31 + 0.03 x:

c. the relationship between x and y is positive.

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E.

c. {2, 4, 6, 8, 10}

A random sample of 150 students has a grade point average with a mean of 2.86 and with a population standard deviation of 0.78. Construct the confidence interval for the population mean, μ. Use a 98% confidence level.

d. (2.71, 3.01)

Which of the following is not an element of descriptive statistical problems?

predictions are made about a larger set of data

A student randomly selects 22 CDs at a store. The mean is $8.5 with a standard deviation of $1.25. Construct a 95% confidence interval for the population standard deviation, Assume the data are normally distributed.

($0.96, $1.79)

The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 200 circuits is tested, revealing 8 defectives. Find a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool.

(0.013, 0.067)

A survey of 200 homeless persons showed that 35 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans. Let z0.05 = 1.65.

(0.13, 0.22)

The mean replacement time for a random sample of 21 microwave ovens is 8.6 years with a standard deviation of 2.7 years. Construct the 98% confidence interval for the population variance, Assume the data are normally distributed

(3.9, 17.7)

Assume that the heights of women are normally distributed. A random sample of 35 women have a mean height of 62.5 inches and a standard deviation of 2.8 inches. Construct a 98% confidence interval for the population variance,

(4.8, 15.0)

Construct a 95% confidence interval for the population standard deviation of a random sample of 15 men who have a mean weight of 165.2 pounds with a standard deviation of 10.3 pounds. Assume the population is normally distributed.

(7.5, 16.2)

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, X. The probabilities corresponding to the 14 possible values of X are summarized in the given table. Answer the question using the following table. X(girls)

0.029

The probability is 2% that an electrical connector that is kept dry fails during the warranty period of a portable computer. If the connector is ever wet, the probability of a failure during the warranty period is 10%. If 80% of the connectors are kept dry and 20% are wet, what proportion of connectors fail during the warranty period?

0.036

A card game is played in which the player wins if a face card is drawn (king, queen, jack) from a deck of 52 cards. If the player plays 10 times, what is the probability that the number of wins for the player is 5?

0.0444

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be more than 12 minutes?

0.0498

The mean diameter of marbles manufactured at a particular toy factory is 0.850 cm with a standard deviation of 0.010cm. What is the probability of selecting a random sample of 64 marbles that has a mean diameter greater than 0.852 cm?

0.0548

The probability that a tennis set will go to a tie-breaker is 15%. What is the probability that two of three sets will go to tie-breakers?

0.057

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil will be less than 0.285 inches?

0.0668

A normal distribution has mean μ = 60 and standard deviation σ = 6, find the area under the curve between 58 and 63.

0.322

The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 4.5 to 6.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 5.85 millimeters?

0.325

In 2005, the property crime rates (per 100,000 residents) for the 50 states and the District of Columbia had a mean of 3477 and a standard deviation of 747. Assuming the distribution of property crime rates is normal, what percentage of the states had property crime rates between 3362 and 4055?

0.34

The lengths of pregnancies are normally distributed with a mean of 269 days and a standard deviation of 25 days. If 64 women are randomly selected, find the probability that they have a mean pregnancy between 268 days and 271 days.

0.3644

Police estimate that 22% of drivers drive without their seat belts. If they stop 4 drivers at random, find the probability that all of them are wearing their seat belts.

0.3701

In 2006, the General Social Survey asked 4,491 respondents how often they attended religious services. The responses were as follows: Frequency

0.398

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 4.5 to 7.5 millimeters. Any ball bearing with a diameter of over 6.25 millimeters or under 4.55 millimeters is considered defective. What is the probability that a randomly selected ball bearing is defective?

0.433

Let X represent the amount of time it takes a student to park in the library parking lot at the university. If we know that the distribution of parking times can be modeled using an exponential distribution with a mean of 4 minutes, find the probability that it will take a randomly selected student between 2.5 and 10 minutes to park in the library lot.

0.453176

The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below: 0.165 0.114 0.503 0.392 0.579 0.311. Find the range of data.

0.465

A machine is set to pump cleanser into a process at the rate of 5 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 4.5 to 7.5 gallons per minute. Find the probability that between 4.8 gallons and 6.2 gallons are pumped during a randomly selected minute.

0.47

The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by Determine the value of

0.5

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 48 minutes and a standard deviation of 10 minutes. A random sample of 36 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?

0.500

Assume that X has a normal distribution with the mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 15.2.

0.5000

A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls followed a normal distribution with an average of $1000 per month and a standard deviation of $65 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, what is the probability that a randomly selected month had a PCE of between $875 and $1010?

0.5339

The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 10% of people with home-based computers have access to on-line services. Suppose that 8 people with home-based computers were randomly and independently sampled. What is the probability that at least 1 of those sampled have access to on-line services at home?

0.5695

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-a < Z < a) = 0.4314, find a.

0.57

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 6.5 minutes. What is the probability that a randomly selected caller is placed on hold fewer than 7.5 minutes?

0.684579

The weights of the fish in a certain lake are normally distributed with a mean of 15 lb and a standard deviation of 5. If 4 fish are randomly selected, what is the probability that the mean weight will be between 12.6 and 18 lb.

0.7164

An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. The Altigauge Manufacturing Company makes 85% of the ELTs, the Bryant Company makes 10% of them, and the Chartair Company makes the other 5%. The ELTs made by Altigauge have a 3% rate of defects, the Bryant ELTs have a 5% rate of defects, and the Chartair ELTs have a 10% rate of defects. If a randomly selected ELT is then tested and is found to be defective, find the probability that it was made by the Altigauge Manufacturing Company.

0.718

In a study of pleas and prison sentences, it is found that 35% of the subjects studied were sent to prison. Among those sent to prison, 30% chose to plead guilty. Among those not sent to prison, 50% chose to plead guilty. If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison.

0.756

In 2006, the percent of the voting-age population that was registered to vote for the 50 states and the District of Columbia had a mean of 63.5% with a standard deviation of 7.4. Assuming that the distribution is normal, what percentage of states had between 53 and 72 percent of it's voting-age population who were registered to vote?

0.797

The New York State Health Department reports a 12% rate of the HIV virus for the "at-risk" population. Under certain conditions, a preliminary screening test for the HIV virus is correct 99% of the time. If someone is randomly selected from the at-risk population, what is the probability that they have the HIV virus if it is known that they have tested positive in the initial screening?

0.931

A survey of senior citizens at a doctor's office shows that 65% take blood pressure-lowering medication, 38% take cholesterol-lowering medication, and 7% take both medications. What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication?

0.96

A basketball player is asked to shot free throws in sets of four. The player shoots 100 sets of 4 free throws. The probability distribution for making a particular number of free throws id given below. Determine the standard deviation for this discrete probability distribution. x

1.32

On a multiple choice test with 12 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the random variable X, the number of correct answers.

1.500

The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 11. Find the standard deviation for the random variable X, the number of seeds germinating in each batch.

1.52

A die is rolled 10 times and the number of times that two shows on the up face is counted. If this experiment is repeated many times, find the mean for the random variable X, the number of twos thrown out of ten tosses.

1.67

A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9 to 13.5 gallons per minute. Find the variance of the distribution.

1.6875

A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proprtion by more than 4%? A previous study indicates that the proportion of left-handed golfers is 10%.

217

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the σ = 3.3 mg claimed by the manufacturer. Assume that a hypothesis test of the given claim will be conducted. Identify the type II error for the test.

3.3 mg when it is actually different from 3.3 mg.

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 51 minutes and a standard deviation of 6.5 minutes. Find the number of minutes, m, for which the probability that a customer spends less than m minutes in the supermarket is 0.20.

45.5

In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. How large a sample must he select if he wants to be 99% confident that the true average time is within 8 minutes of the sample average? Assume the standard deviation of all times is 21 minutes. Let z0.005 = 2.58.

46

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students' scores on the verbal reasoning portion of the GRE follow a normal distribution with a standard deviation of 120. Suppose a random sample of 10 students took the test, and the standard deviation of their scores is 97.2. What is the test statistic for the test H1: σ ≠120.

5.90

Suppose that X has a discrete uniform distribution on the integers 1 to 15. Find 3V(X).

56

A new apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than 0.05 to ensure proper inoculation. A random sample of 25 injections resulted in a variance of 0.118. What is a test statistic for the test H1: σ> 0.05.

56.64

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid and have no private health insurance. The ages of 25 uninsured senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 Identify the first quartile of the ages of the uninsured senior citizens.

65.5

Past experience indicates that the standard deviation in the time it takes for a "fast lube" operation to actually complete the lube and oil change for customers is 3.00 minutes. The manager wishes to estimate the mean time with 99% confidence and a total width of the two-side confidence interval on mean to be 1 minute. Given this, what must the sample size be?

About 239

Assume that the heights of men are normally distributed. A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of 2.2 inches. Construct a 99% confidence interval for the population standard deviation. Let $$\chi_{0.005,15}^2=32.8;\chi_{0.995,15}^2=4.6$$.

a. (1.5, 4.0)

Construct a 95% confidence interval for the population standard deviation $$\sigma$$ of a random sample of 15 men who have a mean weight of 165.2 pounds with a standard deviation of 10.3 pounds. Assume the population is normally distributed.

a. (7.5, 16.2)

Consider a random sample of 20 observations of two variables X and Y. The following summary statistics are available: Σyi = 12.75,Σxi = 1478, = 143,215.8, and Σxiyi = 1083.67. What is the slope of the sample regression line?

a. 0.0042

A recent study of 60 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.01, the critical value for the test to determine whether the true population correlation coefficient is zero is:

a. 2.66

The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of

a. descriptive statistics.

The standard error of the population proportion will become larger

as population proportion approaches 0.50.

In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation, $$\sigma,$$ is 2.4. Construct the 95% confidence interval for the population mean.

b. (61.9, 64.9)

A normal distribution has mean μ = 60 and standard deviation = 6, find the area underthe curve between 58 and 63.

b. 0.322

When considering area under the standard normal curve, decide whether the area between z = -1.5 and z = 1.1 is bigger than, smaller than, or equal to the area between z = -1.1 and z = 1.5.

b. equal to

When considering area under the standard normal curve, decide whether the area to the right of z = 2 is bigger than, smaller than, or equal to the area to the right of z = 2.5.

bigger than

The table contains the weights and heights of nine randomly selected adults. Compute the correlation coefficient.

c. 0.73

Construct the boxplot for the given data below: 3, 3, 5, 6, 4, 9, 8, 9, 6.

d.

Suppose we have the following information from a simple regression: = 107.4, = -14.30, se()= 2.8, se()= 2.4, n = 200. What is the value of the test statistic for testing H0: ?

e. -5.96

The table contains the weights and heights of nine randomly selected adults. Compute the correlation coefficient.

e. 0.73

The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales and the years of experience of 8 randomly selected salespeople. These data are listed below. Years of Experience 0 2 7 4 9 5 5 8 Sales 7 7.7 15 8.5 15 7 8 12 Determine the correlation coefficient.

e. 0.81

If a sample of n = 40 people is selected and the sample correlation between two variables is r = 0.468, what is the test statistic value for testing whether the true population correlation coefficient is equal to zero?

e. 3.26

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. Claim: μ = 78. Sample data: n = 24, s = 15.3. The sample data appear to come from a population that is normally distributedand σ is unknown.

Student t

An article stated that students in FPT university system take an average of 4.5 years to finish their undergraduate degrees. Suppose you believe that the average time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Assume that time to finish their undergraduate degrees is normally distributed. Calculate the value of the test statistic and the critical values for this test statistic. Use a significance level of 0.05. [file:3645.jpg]

Test statistic: 3.5 and critical value: 1.645

Suppose X is a uniform random variable over the interval [20, 90]. Find the probability that a randomly selected observation is between 23 and 85.

a. 0.89

Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A previous random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled if a 95% confidence interval was desired to estimate the true proportion to within 5%?

a. 379

The probability that a student at a certain college is male is 0.45. The probability that a student at that college has a job off campus is 0.33. The probability that a student at the college is male and has a job off campus is 0.15. If a student is chosen at random from the college, what is the probability that the student is male or has an off campus job?

b. 0.63

Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Use μ, the true average mileage of the Libra. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

b. H0: μ = 30 H1: μ > 30

Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten? Create the sample space of possible outcomes.

b. LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD

The following table shows the political affiliation of voters in one city and their positions on stronger gun control laws. Favor Oppose Republican 0.09 0.26 Democrat 0.22 0.2 Other 0.11 0.12 What is the probability that a voter who favors stronger gun control laws is a Republican?

c. 0.214

A random number generator is set top generate integer random numbers between 1 and 10 inclusive following a uniform distribution. What is the probability of the random number generator generating a 7?

c. 1/10

A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 90% confident that the true mean is within 4 ounces of the sample mean? The standard deviation of the birth weights is known to be 6 ounces.

c. 7

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces. Find the number of ounces above which 80% of the dispensed sodas will fall.

c. 8.6

Construct the cumulative frequency distribution that coressponds to the given frequency distribution

d.

Which of the following is always true?

If A and B are disjoint, then they cannot be independent.

Given events A and B with probabilities P(A) = 0.75 and P(B) = 0.15, are A and B mutually exclusive?

cannot be determined

A single six-sided die is rolled. Find the probability of rolling a number less than 3.

0.333

(See picture) [file:2162.jpg]

0.4562

Hahn is having his sixth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%. Create the sample space of possible outcomes (Normal: N, Runt: R).

NNR NNN

Which statement is true?

Probability models quantify the risks involved in decisions made every day

Which of the following is not true of statistics?

Statistics is used to answer questions with 100% certainty.

In a recent study of 49 eighth graders, the mean number of hours per week that they watched television was 18.6 with a population standard deviation of 6.8 hours. Find the 95% confidence interval for the population mean.

(16.7, 20.5)

(See picture) [file:2247.jpg]

0.0027

(See picture) [file:2286.jpg]

0.894

The number of weeds that remain living after a specific chemical has been applied averages 1.21 per square yard and follows a Poisson distribution. Based on this, what is the probability that a 1 square yard section will contain less than 5 weeds?

0.9920

A random number generator is set top generate integer random numbers between 0 and 9 inclusive following a uniform distribution. What is the probability of the random number generator generating a 6?

1/10

A pair of dice is thrown twice. What is the probability of getting totals of 7 and 11?

1/54

The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. 105, 145, 190, 140, 175

33.05

(See picture) [file:2279.jpg]

4.098

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 360 hours and a standard deviation of 5 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation of the mean?

68%

Suppose X is a uniform random variable over the interval [40, 70]. Find the standard deviation of X.

8.66

Suppose that P(A

B) = 0.3 and P(B) = 0.4. Determine P(A' and B). | 0.28

Suppose that P(A

B) = 0.3 and P(B) = 0.4. Determine P(A' and B). | a. 0.28

Two events A and B are said to be _________ if P(A

B) = P(A) or if P(B|A) = P(B). | independent

If the coefficient of correlation is 0.78, what does the coefficient of determination equal?

b. 0.6084

If Z is a standard normal variable, find the the probability that Z is less than 1.13.

b. 0.8708

In its standardized form, the normal distribution

b. be used to approximate discrete probability distributions.

Given the least squares regression line = -2.88- 1.77x and a coefficient of determination of 0.64, the coefficient of correlation is:

c. -0.8

Determine the test statistic to test the claim about the population proportion p > 0.51 given n = 50 and Use

None of the other choices is true

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. Claim: μ = 119. Sample data: n = 45, s = 15.2. The sample data appear to come from a populationthat is not normally distributedwith unknown μ and

Normal

Consider a random sample of 20 observations of two variables X and Y. The following summary statistics are available: Σyi = 12.75,Σxi = 1478, = 143,215.8, and Σxiyi = 1083.67. What is the slope of the sample regression line?

c. 0.0042

Suppose that a random sample of 10,000 (X, Y) pairs yielded: = 10.4, se()= 21.2, se()= 2.4. What is the value of the test statistic for testing H0: ?

c. 0.019

Use the given information to find the P-value. The test statistic in a left-tailed test is z = -1.83.

c. 0.0336

LetZ is a standard normal variable, find the probability that Z lies between -1.10 and -0.36.

c. 0.2237

LetZ is a standard normal variable, find theprobability that Z lies between -2.41 and 0.

c. 0.4920

For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean.

c. 2.41%

Which of the following cannot be a probability?

c. 4/3

The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 3 randomly selected adults. Age, x 42 45 49 Pressure, y 118 122 125 Calculate the test statistic to test the claim ρ = 0. Round answers to three decimal places.

c. 5.913

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective?

d. 0.92

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be less than 15 minutes?

d. 0.9765

The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed.

d. 55.8

Elaine gets quiz grades of 67, 64, and 87. She gets a 84 on her final exam. Find the mean grade if the quizzes each count for 15% and her final exam exam counts for 55% of the final grade.

d. 78.9

A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours. Based on these sample data, which of the following is the regression equation?

d. = 5.67 + .048x.

If two balanced die are rolled, the possible outcomes can be represented as follows. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Determine the probability that the sum of the dice is 4 or 12.

a. 1/9

A 99% confidence interval estimate can be interpreted to mean that

a. Both of the above.

The grade point averages for 10 randomly selected high school students are listed below, which implies a sample mean of 2.54 and a sample standard deviation of 1.11. Assume the grade point averages are normally distributed. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 Find a 98% confidence interval for the true mean.

(1.55, 3.53)

If P(A) = 0.45, P(B) = 0.25, and P(B

A) = 0.45, are A and B independent? | no

LetZ is a standard normal variable, find the the probability that Z lies between 0 and 3.01.

0.4987

According to a college survey, 18% of all students work full time. Find the standard deviation for the random variable X, the number of students who work full time in samples of size 35.

2.27

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. Find the variance for the probability distribution. x

2.41

Assume that P(C) = 0.5 and P(D) = 0.3. If C and D are independent, find P(C and D).

0.15

A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 4.3. Find the probability that on a randomly selected trip, the number of whales seen is 3.

0.1798

According to the 2003 National Survey on Drug Use and Health, 54.3% of males have never used marijuana. Based on this percentage, what is the expected number of males who have used marijuana for samples of size 100?

45.7

(See picture) [file:3694.jpg]

-0.93

Suppose that 11% of people are left handed. If 6 people are selected at random, what is the probability that exactly 2 of them are left handed?

0.1139

Suppose the cumulative distribution function of the random variable X is Find the value of P(X>5).

0.16

A tennis player makes a successful first serve 53% of the time. If she serves 6 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

0.3091

For two events A and B, P(A) = 0.4, P(B) = 0.5. Then P(A or B) equals

0.7, if A and B are independent.

(See picture) [file:1973.jpg]

1.25

A random sample of 40 students has a mean annual earnings of $3120 and a population standard deviation of $677. Construct the confidence interval for the population mean, μ. Use a 95% confidence level.

c. ($2910, $3330)

Suppose we have the following information from a simple regression: = 117.4, = -17.29, n = 300, = 4.3, SST = 17000, and SSE = 10000. What is the correlation coefficient?

c. -0.642

Find the critical value or values of $$\chi^2$$ based on the given information. H1: σ > 26.1 n = 9 α = 0.01

c. 20.090

The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Use the regression equation to predict the life span, y, for a gestation period of 6 months, x. Assume the variables x and y have a significant correlation. Gestation, x 8 2.1 3.8 Life span, y 30 12 10

c. 21.97

For a standard normal distribution, find the percentage of data that are more than 1 standard deviation away from the mean.

c. 31.74%

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 50 to 70. What is the mean outcome of this experiment?

c. 60

Given that events A and B are mutually exclusive and P(A) = 0.5 and P(B) =0.7, are A and B independent?

no

One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.7 million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1.1 million.

d. approximately 1

A researcher claims that 62% of voters favor gun control. Assume that a hypothesis test of the given claim will be conducted. Identify the type II error for the test.

gun control is 62% when it is actually different than 62%.

The age distribution of students at a community college is given below. Age (years)

0.454

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1000. A random sample of 59 individuals resulted in an average income of $21000. What is the width of the 90% confidence interval?

$428.32

[file:3641.jpg]

(ii)

Bon Air Elementary School has 300 students. The principal of the school thinks that the average IQ of students at Bon Air is at least 110. To prove her point, she administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 108 with a standard deviation of 10. What is the value of the test statistic? Assume the IQ of students is normally distributed.

-0.894

Find the test statistic t0 for a sample with n = 20, = 7.5, s = 1.9, and if H1: μ < 8.3. Round your answer to three decimal places.

-1.883

If Z is a standard normal variable, find the the probability that Z is less than 1.13.

0.8708

An electrical firm manufactures a certain type of light bulb that has a mean light of 1,900 hours and a standard deviation of 200 hours. Find the probability that a random sample of 100 bulbs will have an average life of not more than 1,975 hours and not less than 1,860 hours.

0.9772

Find the standard deviation for the probability distribution. x

0.98

Suppose that X has a discrete uniform distribution on the integers 0 through 5. Determine the mean of the random variable Y = 4X

10

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 26 minutes and a standard deviation of 3 minutes. A random sample of 30 cars is selected. So, 90% of the sample means will be greater than what value?

28.5 minutes

[file:3579.jpg]

598, 600, 602, 604, 605

Find the mode for the sample composed of the observations 4, 5, 6, 6, 6, 7, 7, 8, 8, 5.

6

Find the critical value or values of based on the given information. H1: σ < 0.629 n = 21 = 0.025

9.591

Suppose that P(A

B) = 0.6, P(A) = 0.5 and P(B) = 0.1. Find the value of P(B|A). | 0.12

A 99% confidence interval estimate can be interpreted to mean that (i) if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. (ii) we have 99% confidence that we have selected a sample whose interval does include the population mean.

Both of (i) and (ii)

In a binomial distribution with 10 trials, which of the following is true?

a. P(x > 7) = P(x ≥ 8)

To calculate the probability of obtaining three aces in eight draws of a card with replacement from an ordinary deck, we would use the

b. binomial distribution.

Which of the following is always true for a normal distribution?

P(2< x ≤ 8) = P(2 ≤ x < 8)

In a binomial distribution with 10 trials, which of the following is true?

P(x > 7) = P(x ≥ 8)

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?

a. 0.029

The owner of a football team claims that the average attendance at games is over 67,000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

The error of rejecting the claim that the mean attendance is at most 67,000, when it really is at most 67,000.

A cereal company claims that the mean weight of the cereal in its packets isdifferent from 14 oz. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

The error of rejecting the claim that the mean weight is 14 oz. when it really is 14 oz.

An article stated that students in FPT university system take an average of 4.5 years to finish their undergraduate degrees. Suppose you believe that the average time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Assume that time to finish their undergraduate degrees is normally distributed. Calculate the value of the test statistic and the critical values for this test statistic. Use a significance level of 0.05.

Test statistic: 3.5 and critical value: 1.645

Sample variance is

a statistic.

Find the origin data from the sterm-and-leaf plot

a.

If sample points A, B, C, and D are the only possible outcomes of an experiment, find the probability of D using the table below. .

a.

Which of the following is a continuous quantitative variable?

The volume of gasoline that is lost to evaporation during the filling of a gas tank.

An insurance company analyst is interested in analyzing the dollar value of damage in automobile accidents. She collects data from 115 accidents, and records the amount of damage as well as the age of the driver. The results of her regression analysis are listed below. On average, what would be the dollar value of an accident involving a 30-year-old driver?

a. $12,824.722

An electrical firm manufactures a certain type of light bulb that has a mean light of 1,800 hours and a standard deviation of 200 hours. Find the probability that a random sample of 100 bulbs will have an average life of more than 1,825 hours.

a. 0.1056

Fifty percent of the people that get mail-order catalogs order something. Find the probability that only three of 10 people getting these catalogs will order something.

a. 0.117

Assume that X has a normal distribution with the mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 16.1.

a. 0.1587

The grade point averages for 10 randomly selected high school students are listed below. Assume the grade point averages are normally distributed. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 Find a 98% confidence interval for the true mean.

a. (1.55, 3.53)

A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

a. 0.172

Police estimate that 25% of drivers drive without their seat belts. If they stop 6 drivers at random, find the probability that all of them are wearing their seat belts.

a. 0.178

A batch of 500 machined parts contains 10 that do not conform to customer requirements.Parts are selected succesively, without replacement, until a nonconforming part is obtained. Determine the range (possible values) of the random variable giving the number of parts selected.

[1, 491]

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(0.2 < Z < a) = 0.2314, find a.

a. 0.8805

You want to explore the relationship between the grades students receive on their first quiz (X) and their first exam (Y). The first quiz and test scores for a sample of 11 students reveal the following summary statistics: = 330.5, sx = 2.03, and sy = 17.91 What is the sample correlation coefficient?

a. 0.909

The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 11. Find the standard deviation for the random variable X, the number of seeds germinating in each batch.

a. 1.52

A die is rolled 18 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.

a. 1.581

Find the critical value or values of $$\chi^2$$ based on the given information. H1: σ > 3.5 n = 14 α = 0.05

a. 22.362

A survey of the 9225 vehicles on the campus of State University yielded the following circle graph Find the number of hatchbacks. Round the result to the nearest whole number .

a. 2860

Find the variance of the given data. Round your answer to one more decimals than the original data.

a. 3.96

Find the mode(s) for the given data

a. 6.8 and 6.5

For several customers at the local bookstore, the scatter diagram compares the weight of their books (y) and the number of pages in them(x) is shown below. State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables.

a. Positive correlation

The amount of corn chips dispensed into a 20-ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 20.5 ounces and a standard deviation of 0.2-ounce. Suppose 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags exceeded 20.6 ounces.

a. approximately 0

A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: = 50,000 + 6x. This implies that:

a. an increase of $1 in advertising is expected to result in an increase of $6000 in sales.

In a regression problem the following pairs of (x, y) are given: (2, 1), (3,-1), (2, 0), (4,-2) and (4, 2). That indicates that the:

a. coefficient of correlation is 0.158

A random sample of 150 students has a grade point average with a mean of 2.86 and with a standard deviation of 0.78. Construct the confidence interval for the population mean, $$\mu,$$ if $$\alpha = 0.02$$. Let $$z_{0.01}=2.33;z_{0.02}=2.05;t_{0.01,149}=2.35;t_{0.02,149}=2.07$$.

b. (2.71, 3.01)

If the least squares equation is = 10 + 8X, then the value of8 (the coefficient of x)indicates:

a. for each unit increase in X, Y increases on average by 8.

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.09 for a right-tailed test.

b. +1.34

When considering area under the standard normal curve, decide whether the area between z = -0.2 and z = 0.2 is bigger than, smaller than, or equal to the area between z = -0.3 and z = 0.3.

a. smaller than

For the data in the table below, what is the value of the test statistic for testing x 15 21 16 30 y 67 80 85 78

b. -0.38

When is the correlation coefficient zero?

a. when there is no linear correlation

For large numbers of degrees of freedom, the critical χ2 values can be approximated as follows: χ2 = (z + )2, where k is the number of degrees of freedom and z is the critical value. To find the lower critical value, the negative z-value is used, to find the upper critical value, the positive z-value is used. Use this approximation to estimate the critical value of χ2 in a right-tailed hypothesis test with n =125 and α = 0.01.

a. χ2 ≈ 162.833

Construct the relative frequency distribution that corresponds to given frequency distribution

b.

Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. Productivity,x 3 5 8 2 1 Dexterity,y 9 3 9 4 7$$ Find the equation of the regression line.

b. $$\hat y = 5.49+0.24x$$

In a random sample of 60 computers, the mean repair cost was $150 with a population standard deviation of $36. Construct a 99% confidence interval for the population mean.

b. ($138, $162)

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. Claim: μ = 78. Sample data: n = 24, $$\overline{x} = 101,$$ s = 15.3. The sample data appear to come from a population with a distribution that is very far from normal, and σ is unknown.

b. Neither

For a group of English students at the local junior college, the scatter diagram compares the number of incorrect answers on a test they took (y) and the length of the pencil used to take the test (x). State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables.

b. No correlation

A sample of10 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 15210, = 17150, = 2599. What is the value of the coefficient of determination?

b. None of the other choices is true

If either event A or event B must occur, then events A and B are said to be

b. None of the others.

We have created a 95% confidence interval for $$\mu$$ with the result (10, 15). What decision will we make if we test $$H_0: \mu =16$$ versus $$H_1: \mu eq 16$$ at $$\alpha= 0.05$$?

b. Reject $$H_0$$ in favor of $$H_1$$.

Given the size of a human's brain, x, and their score on an IQ test, y, would you expect a positive correlation, a negative correlation, or no correlation?

b. no correlation

The time for a worker to assemble a component is normally distributed with mean 15 minutes and variance 4. Denote the mean assembly times of 16 day-shift workers and 9 night-shift workers by $$\overline{X}$$ and $$\overline{Y}$$, respectively. Assume that the assembly times of the workers are mutually independent. The distribution of $$\overline{X} $$- $$\overline{Y}$$ is

b. normal with mean 0 and standard deviation 5/6.

We can show that, when the null hypothesis H0: ρ = 0 is true and the random variables have a joint normal distribution, then the random variable which is used to test the hypothesis that there is no linear association in the population between a pair of random variables, follows the:

b. student's t distribution.

Identify the choice that best completes the statement Given the least squares regression line = 12.31 + 0.03 x:

b. the relationship between x and y is positive.

A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n =1158 subjects with 30% saying that they play a sport. Find the value of the test statistic z using $$z=\frac{\overline{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$$

c. -13.61

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 4.5 to 6.5 millimeters. Any ball bearing with a diameter of over 6.25 millimeters or under 4.75 millimeters is considered defective. What is the probability that a randomly selected ball bearing is defective?

c. 0.25

An airline reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservations, find the probability that there will be fewer than 20 no-shows.

c. 0.251

If a random variable has the normal distribution with μ = 30 and σ = 5, find the probability that it will take on the value between 31 and 35.

c. 0.262

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be more than 5 minutes?

c. 0.2865

A group of students were asked if they carry a credit card. The responses are listed in the table. If a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places.

c. 0.833

Suppose X is a uniform random variable over [10, 70]. Find the probability that a randomly selected observation is between 13 and 65.

c. 0.87

A greenhouse is offering a sale on tulip bulbs because they have inadvertently mixed pink bulbs with red bulbs. If 40% of the bulbs are pink and 60% are red, what is the probability that at least one of the bulbs will be pink if 4 bulbs are purchased?

c. 0.8704

If two balanced die are rolled, the possible outcomes can be represented as follows. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Determine the probability that the sum of the dice is 7.

c. 1/6

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?

c. 12

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 6%?

c. 378

Given a sample with r = 0.833, n = 12, and = 0.05, determine the test statistic t0 necessary to test the claim ρ = 0. Round answers to three decimal places.

c. 4.761

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure that lies within 3 standard deviations of the mean?

c. 99.7%

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 2 in every one thousand. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

c. H0: p = 0.002 H1: p < 0.002

Survey responses of " good, better, best". which type of data is?

c. Ordinal

The conditional probability of event G, given the knowledge that event H has occurred, would be written as _____.

c. P(G | H)

For several customers at the local bookstore, the scatter diagram compares the weight of their books (y) and the number of pages in them(x) is shown below. State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables.

c. Positive correlation

Which of the following is not true of statistics?

c. Statistics is used to answer questions with 100% certainty.

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 45°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

c. There is sufficient evidence to support the claim that the mean temperature is different from 45°F

When considering area under the standard normal curve, decide whether the area between z = 3 andz = -3 is bigger than, smaller than, or equal to the area betweenz =2.7 and z = 2.9.

c. bigger than

When considering area under the standard normal curve, decide whether the area to the right of z = 2 is bigger than, smaller than, or equal to the area to the right of z = 2.5.

c. bigger than

An indication ofno linear relationship between two variables would be a:

c. coefficient of correlation of 0

Which of the following statements is false i) If X1, X2,...,Xn is a random sample of size n,the sample standard deviation S is nota statistic. ii) The probability distribution of a statistic is called a sampling distribution. iii) A statistic is any function of the observations in a random sample. iv) The sampling distribution of a statistic does not depend on the distribution of the population.

c. i) and iv)

The random variableX represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation for the random variable X. x 0 1 2 3 4 P(x) 3/17 5/17 6/17 2/17 1/17

c. mean: 1.59; standard deviation: 1.09

The height y and base diameter x of five tree of a certain variety produced the following data x 2 4 3 4 y 33 41 96 90 What is the value of the test statistic for testing

d. 0.026

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(Z > c) = 0.1093, find c.

d. 1.23

If $$n = 10$$ and $$p = 0.70$$, then the standard deviation of the binomial distribution is

d. 1.45

A simple regression model has the form: = 10 + 2x. As x increases by one unit, then the value of y will increase by:

d. 2 units

Assume that you are predicting X from Y. Which of the following correlation coefficients would yield predictions with the most error?

d. r = 0.14

For sample sizes greater than 40, the sampling distribution of the mean will be approximately normally distributed

d. regardless of the shape of the population.

Let denote the sample mean of a random sample of size n1 = 16 taken from a normal distribution N(125, 36), and let denote the sample mean of a random sample of size n2 = 25 taken from a different normal distribution N(125, 9). The distribution of is

normal with mean 0 and standard deviation 1.6155

To determine the difference , if any, between two brands of radial tires, 12 tires of each brand are tested. Assume that the lifetimes of both brands of tires come from the same normal distribution N(102000, 33002). The distribution of the difference of the sample mean

normal with mean 0 and standard deviation 1347.22

The process of using sample statistics to draw conclusions about true population parameters is called

statistical inference.

(See picture) [file:2255.jpg]

to = -1.98, fail to reject Ho

(See picture) [file:2262.jpg]

(i)

Calculate the range of the following data set: 7, 8, 4, 1, 4, 15, 5, 8, 5

14

The probability that a person has immunity to a particular disease is 0.6. Find the mean for the random variable X, the number who have immunity in samples of size 26.

15.6

[file:3656.jpg]

16.875

Determine the critical values to test the claim about the population proportion p ≠ 0.325 given n = 42 and Use .

2.575 and -2.575

Let X be a continuous random variable with probability density function defined by What value must k take for this to be a valid density?

2/3

(See picture) [file:3700.jpg]

3.000

Find the mode(s) for the given data

6.8 and 6.5

Assume that the heights of women are normally distributed. A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of 2.5 inches. Construct a 98% confidence interval for the population variance, $$\sigma^2.$$

c. (3.3, 15.6)

Which of the following represents the strongest linear correlation?

c. -0.97

Find z if the normal curve area to the left of z is 0.1611.

c. -0.99

Carter Motor Company claims that its new sedan, the Libra, will average better than 19 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

c. There is sufficient evidence to support the claim that the mean is greater than 19 miles per gallon.

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.09 for a two-tailed test.

±1.695

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.01 for a two-tailed test.

±2.575

(See picture) [file:2084.jpg]

(i)

[file:3646.jpg]

(ii)

Find the standard normal-curve area between z = -1.3 and z = -0.4.

0.2478

A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses) Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing?

a. 20%

Suppose that $$X$$ has the probability density function $$f(x)=1.5x^2$$ for $$-1 Chọn một câu trả lời

d. 0.125

If X is a normal random variable with μ = 50 and σ = 6, then the probability that X is not between 44 and 56 is

d. 0.3174.

Suppose the cumulative distribution of the random variable X is Detemine

0.25

A random sample of 42 students has a mean annual earnings of $1200 and a population standard deviation of $230. Construct a 95% confidence interval for the population mean, μ.

($1130, $1270)

A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed. $6.30 $6.75 $4.25 $3.60 $4.50 $2.80 $8.00 $3.00 $2.60 $5.20 Find the 95% confidence interval for the true mean.

($3.39, $6.01)

The grade point averages for 10 randomly selected high school students are listed below, which implies a sample mean of 2.54 and a sample standard deviation of 1.11. Assume the grade point averages are normally distributed. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 Find a 98% confidence interval for the true mean. [file:2211.jpg]

(1.55, 3.53)

In a recent study of 22 eighth graders, the mean number of hours per week that they watched television was 19.6 with a standard deviation of 5.8 hours. Construct a 90% confidence interval for the population mean. Assume the population has a normal distribution.

(17.47, 21.73)

In a recent study of 22 eighth graders, the mean number of hours per week that they watched television was 19.6 with a standard deviation of 5.8 hours. Construct a 90% confidence interval for the population mean. Assume the population has a normal distribution. [file:2209.jpg]

(17.47, 21.73)

In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6 with a population standard deviation of 5.8 hours. Find the 98% confidence interval for the population mean.

(17.5, 21.7)

A random sample of 40 students has a mean annual earnings of 3120 and a population standard deviation of 677. Construct the confidence interval for the population mean. Use a 95% confidence level. [file:2187.jpg]

(2910, 3330)

Find the test statistic t0 for a sample with n = 10, = 7.9, s = 1.3, and ifH1:µ > 8.0. Round your answer to three decimal places.

-0.243

Among the contestants in a competition are 25 women and 25 men. If 3 winners are randomly selected, what is the probability that they are all men?

0.117

A percentage distribution is given below for the size of families in one U.S. city. Size

0.169

Assume that a procedure yields a binomial distribution with a trial repeated 64 times. Use the binomial probability formula to find the probability of 3 successes given the probability 0.04 of success on a single trial.

0.221

The following table shows the political affiliation of voters in one city and their positions on stronger gun control laws.

0.314

The probability that a house in an urban area will be burglarized is 3%. If 30 houses are randomly selected, what is the probability that none of the houses will be burglarized?

0.4010

Let X be a uniform random variable over the interval [0.1, 5] . What is the probability that the random variable X has a value less than 2.1?

0.408

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the probability that the number favoring the substation is more than 12?

0.6482

Suppose x is a uniform random variable over [10,90]. Find the probability that a randomly selected observation exceeds 26.

0.8

The age distribution of students at a community college is given below. Age (years)

0.903

The distribution of B.A. degrees conferred by a local college is listed below, by major. Major

0.966

An article in Concrete Research presented data on compressive strength $$x$$ and intrinsic permeability $$y$$ of various concrete mixes and cures. Summary quantities are $$n = 14,\sum y_i=572,\sum y_i^2=23,\sum x_i=43, \sum x_i^2=157.42$$, and $$\sum x_i y_i=1697.8$$. Assume that the two variables are related according to the simple linear regression model. Calculate the least squares estimates of the slope.

a. -2.33

The area to the right of z = 1.0 is equal to

a. 0.1587.

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. What proportion of customers having to hold more than 4.5 minutes will hang up before placing an order?

a. 0.22313

Find the standard normal-curve area between z = -1.3 and z = -0.4.

a. 0.2478

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 2.8 minutes. What proportion of callers is put on hold longer than 2.8 minutes?

a. 0.367879

The following table shows the political affiliation of voters in one city and their positions on stronger gun control laws. Favor Oppose Republican 0.11 0.27 Democrat 0.25 0.16 Other 0.15 0.06 What is the probability that a Democrat opposes stronger gun control laws?

a. 0.390

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household do not own 2 cars is:

a. 0.40

The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below: 0.165 0.114 0.503 0.392 0.579 0.311. Find the range of data.

a. 0.465

A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9.5 to 11.5 gallons per minute. What is the probability that at the time the machine is checked it is pumping more than 10.5 gallons per minute?

a. 0.50

The probability that a house in an urban area will be burglarized is 2%. If 29 houses are randomly selected, what is the probability that none of the houses will be burglarized?

a. 0.557

In 2006, the General Social Survey asked 4,491 respondents how often they attended religious services. The responses were as follows: Frequency Number of respondents Never 1020 Less than once a year 302 Once a year 571 Several times a year 502 Once a month 308 Two-three times a month 380 Nearly every week 240 Every week 839 More than once a week 329 What is the probability that a randomly selected respondent attended religious services more than once a year?

a. 0.58

If a random variable has the normal distribution with μ = 30 and σ = 5, find the probability that it will take on the value less than 32.

a. 0.6554

In 2005, the property crime rates (per 100,000 residents) for the 50 states and the District of Columbia had a mean of 3377.2 and a standard deviation of 847.4. Assuming the distribution of property crime rates is normal, what percentage of the states had property crime rates between 2360 and 4055?

a. 0.67

The weights of the fish in a certain lake are normally distributed with a mean of 15 lb and a standard deviation of 6. If 4 fish are randomly selected, what is the probability that the mean weight will be between 12.6 and 18.6 lb.

a. 0.6730

If you were constructing a 99% confidence interval of the normal population mean based on a sample of $$n = 25$$ where the standard deviation of the sample $$s = 0.05$$. What is the critical value? Let $$t_{0.005,24}=2.7969;t_{0.01,24}=2.4922;z_{0.01}=2.33; z_{0.05}=2.58$$.

a. 2.7969

A random sample of 20 observations was made on the diameter of spot welds and the corresponding weld shear strength. Given that r = 0.65, what is the value of test statistic if we want to test the hypothesis that ρ = 0 at a level of significance of 0.05. Let t0.025,18 = 2.1, t0.05,18 = 1.73 and t0.025,19 = 2.09.

a. 3.63

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the Manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month. Miles traveled, x 4 8 10 Sales, y 27 58 61 Calculate the test statistic to test the claim ρ = 0. Round answers to three decimal places.

a. 3.857

Given the equation of a regression line is = 4x - 6, what is the best predicted value for y given x = 9? Assume that the variables x and y have a significant correlation.

a. 30

In simple linear regression, which of the following statements indicates there is no linear relationship between the variables x and y?

a. Coefficient of correlation is 0.0.

For a group of English students at the local junior college, the scatter diagram compares the number of incorrect answers on a test they took (y) and the length of the pencil used to take the test (x). State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables.

a. No correlation

Survey responses of nationalities of survey respondents. which type of data is?

a. Nomial

A sample of10 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 15210, = 17150, = 2599. What is the value of the coefficient of determination?

a. None of the other choices is true

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. Claim: μ = 959. Sample data: n = 25,$$\overline{x} = 951,$$ s = 25. The sample data appear to come from a normally distributed population with σ = 28.

a. Normal

Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, and C are the only sample points in the experiment?

a. P(A) = 0, P(B) = , P(C) =

If we are using the normal approximation to determine the probability of at most 28 successes in a binomial distribution P(x ≤ 28) the normal distribution probability that is used to make the estimate is

a. P(x ≤ 28.5).

The following table gives the total sales (revenue) and profits for 8 retailers. Construct a scatter diagram for the data and state whether sales and profits for these companies have no correlation, a positive correlation, or a negative correlation.

a. Positive correlation

The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by σ = 14.7. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

a. The error of rejecting the claim that the standard deviation is at least 14.7 when it really is at least 14.7.

Which statement is true for the scores of 1, 2, 3, 4, 5, 5, 7, 8, 9, and 10?

a. The mean is greater than the median.

Which of the following is true about the sampling distribution of the sample mean?

a. The mean of the sampling distribution is always μ.

Determine whether the given conditions justify testing a claim about a population mean μ. The sample size is n = 17, σ is not known, and the original population is normally distributed.

a. Yes

The peak shopping time at home improvement store is between 8-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 150 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that a sapmle of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store.

a. number of items - discrete; total time - continuous

Identify the choice that best completes the statement Given the least squares regression line = 12.31 + 0.03 x:

a. the relationship between x and y is positive.

Suppose that you are interested in the relationship between the return on a stock this year (Y), compared to the return the year before (X). From a sample of 12 firms, you have collected the following information: Σxi = 217, Σyi = 131.7, Σxiyi = 1932.5, Σ(xi)2 = 689, Σ(yi)2 = 1321.5. What is the sample correlation coefficient between X and Y?

b. -0.76

Given the least squares regression line = -2.88- 1.77x and a coefficient of determination of 0.64, the coefficient of correlation is:

b. -0.8

A study of the amount of time it take a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 9.1 hours.

b. 0.0069

Car batteries produced by company A have a mean life of 3.5 years with a standard deviation of 0.4 years. A similar battery producted by company B has a mean life of 3.3 years and a standard deviation of 0.3 years. What is the probability that a random sample of 25 batteries from company A will have a mean life of at least 0.4 years more thanthe mean life of a sample of 36 batteries from company B?

b. 0.0166

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1900 miles. What is the probability a certain tire of this brand will last between 56,010 miles and 56,580 miles?

b. 0.0180

Use the given information to find the P-value. The test statistic in a left-tailed test is z = -2.05.

b. 0.0202

A random sample of n = 25 observations was made on the time to failure of an electronic component and the temperature in the application environment in which the component was used. Given that = 0.4, = 1.50, se()= 7.68, se()= 12.4. What is the value of the test statistic for testing H0: ?

b. 0.04

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income over $25,000 a year is:

b. 0.48

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine?

b. 0.511

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-a < Z < a) = 0.4314, find a.

b. 0.57

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household own 2 cars is:

b. 0.69

Suppose x is a uniform random variable over the interval [40, 50]. Find the probability that a randomly selected observation exceeds 43.

b. 0.7

The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is

b. 0.733

Consider the following pairs of observations: x 2 3 5 5 7 6 y 1.3 1.5 2.2 2.3 2.7 1.9 Find the value of the coefficient of correlation.

b. 0.897

According to a college survey, 22% of all students work full time. Find the standard deviation for the random variable X, the number of students who work full time in samples of size 16.

b. 1.66

Recently, an automobile insurance company performed a study of a random sample of 38 of its customers to determine if there is a positive relationship between the number of miles driven and the age of the driver. The sample correlation coefficient is r = 0.59. Given this information, which of the following is appropriate critical value for testing the null hypothesis at an alpha = 0.05 level?

b. 1.688

Given a sample with r = 0.329, n = 30, and = 0.10, determine the test statistic to test the claim ρ = 0. Round answers to three decimal places

b. 1.844

Compute the critical value $$z_{\alpha/2}$$ that corresponds to a 94% level of confidence.

b. 1.88

A researcher claims that 62% of voters favor gun control.Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

b. H0: p = 0.62 H1: p ≠ 0.62

In a simple linear model, testing H0 : = 0 is the same as testing:

b. H0: β1 = 0

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

b. H0: μ = 14 H1: μ < 14

A T.V. show's executives raised the fee for commercials following a report that the show received a " No.1" rating in a survey of viewers. What type of the description is?

b. Observation study

Jared was working on a project to look at global warming and accessed an Internet site where he captured average global surface temperatures from 1866. Which of the four methods of data collection was he using?

b. Retrospective study

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

b. The error of rejecting the claim that the mean weight is at least 14 oz. when it really is at least 14 oz.

The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed below. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 What is the effect on the width of the confidence interval if the sample size is increased to 20?

b. The width decreases.

Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene dominates. List the possible outcomes. W = white and B = black Create the sample space of possible outcomes.

b. WW, BW

Determine whether the given conditions justify testing a claim about a population mean μ. The sample size is n = 25,σ = 5.93, and the original population is normally distributed.

b. Yes

A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: = 50,000 + 6x. This implies that:

b. an increase of $1 in advertising is expected to result in an increase of $6000 in sales.

To calculate the probability of obtaining three aces in eight draws of a card with replacement from an ordinary deck, we would use the

binomial distribution.

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2.

c. (77.29, 85.71)

The weight and systolic blood pressure of 4 randomly selected males in the age group 25 to 30 are shown in the following table. Assume that weight and blood pressure are jointly normally distributed. Weight, x 50 62 67 55 Pressure, y 90 110 120 90 What is the value of the test statistic for testing

c. -0.44

For a sample of 10 observations, you have the following information: Σxi = 253, Σyi = 172.2, Σxiyi = 643.4, Σ(xi)2 = 696, Σ(yi)2 = 152.2. What is the sample correlation coefficient between X and Y?

c. -0.93

Suppose we have the following information from a simple regression: = 107.4, = -14.39, se()= 2.8, se()= 2.4, n = 200. What is the value of the test statistic for testing H0: ?

c. -1.071

The height y and base diameter x of five tree of a certain variety produced the following data x 2 4 3 4 y 33 41 96 90 What is the value of the test statistic for testing

c. 0.026

It has been found that 40% of the employees who complete a sequence of executive seminars go on to become vice presidents. Assume that 10 graduates of the program are randomly selected, find the probability that from two to four become vice presidents. (Note: please give the answer as a real number accurate to4 decimal places after the decimal point.)

c. 0.034

Use the given information to find the P-value. The test statistic in a right-tailed test is z = 1.43.

c. 0.0764

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n = 64, x = 3, p = 0.04

c. 0.221

Let X be a uniform random variable over the interval [0.1, 5] . What is the probability that the random variable X has a value less than 2.1?

c. 0.6897

The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 20% of people with home-based computers have access to on-line services. Suppose that 15 people with home-based computers were randomly and independently sampled. What is the probability that at least 1 of those sampled have access to on-line services at home?

c. 0.9648

Assume that blood pressure readings are normally distributed with a mean of 124 and a standard deviation of 6.4. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 126.

c. 0.9938

The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly selected, what is the mean of the number of houses burglarized?

c. 1

A simple regression model has the form: = 10 + 2x. As x increases by one unit, then the value of y will increase by:

c. 2 units

You want to explore the relationship between the grades students receive on their first two exams. For a sample of 17 students, you find a correlation coefficient of 0.47. What is the value of the test statistic for testing H0: ρ = 0 vs. H1: ρ 0 ?

c. 2.06

A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequence histogram for the systolic blood pressure readings for those people aged between 25 and 40. The blood pressure reading were given to the nearest whole number. Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading between 110 and 119 inclusive?

c. 35%

Which of the following statements is true regarding the coefficient of correlation?

c. All of the others

Which of the following is not an element of descriptive statistical problems?

c. predictions are made about a larger set of data

For some positive value of $$x$$, the probability that a standard normal variable is between 0 and $$x$$ is 0.1255. What is the value of $$x$$? Let $$P(Z>0)=0.5; P(Z<0.32) = 0.6255; P(Z<0.99)=0.8389$$.

d. 0.32

Find the variance for the given sample data 53 52 75 62 68 58 49 49

d. 89.6

A sample of 28 teachers had mean annual earnings of $3450 with a standard deviation of $600. Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution.

($3218, $3682)

A local bank needs information concerning the checking account balances of its customers. A random sample of 18 accounts was checked. The mean balance was $600.70 with a standard deviation of $196.20. Find a 98% confidence interval for the true mean. Assume that the account balances are normally distributed.

($481.85, $719.55)

In a random sample of 120 computers, the mean repair cost was $55 with a population standard deviation of $12. Construct a 99% confidence interval for the population mean.

($52, $58)

The world's smallest mammal is the bumblebee bat. Such bats are roughly the size of a large bumblebee. A sample of the weights for 5 randomly selected bats has standard deviation of 0.33. Assume that the weights of the bats are normally distributed. Construct a 98% confidence interval of the standard deviation of weights for all such bats. Let and

(0.18; 1.21)

Find the standard normal-curve area to the left of z = -0.54.

0.2946

Assume that the weights of quarters are normally distributed with a mean of 5.70 g and a standard deviation 0.062 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected?

2.67%

Suppose that X has a discrete uniform distribution on the integers 2 to 5. Find V(4X).

20

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below: 95, 38, 221, 122, 258, 237, 233. Find the median number of newspapers sold

221

Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A previous random sample of 4000 citizens yielded 2500 who are in favor of gun control legislation. How many citizens would need to be sampled if a 94% confidence interval was desired to estimate the true proportion to within 5%?

332

A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequence histogram for the systolic blood pressure readings for those people aged between 25 and 40. The blood pressure reading were given to the nearest whole number. Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading between 110 and 119 inclusive?

35%

A university is interested in estimating the mean time that students spend at the student recreation center per week. A previous study indicated that the standard deviation in time is about 30 minutes per week. If the officials wish to estimate the mean time within 8 minutes with a 90 percent confidence, what should the sample size be?

39

Find the variance for the given data. Round your answer to one more decimals than original data 1, 4, -5, -9, and 6

39.3

The owner of a fish market determined that the weights of catfish are normally distributed with the average weight for a catfish is 3.2 pounds with a standard deviation of 0.6 pound. A citation catfish should be one of the top 5% in weight. At what weight (in pounds) should the citation designation be established?

4.19

The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 2.1. Based on this, how many defects should be expected if 2 containers are inspected?

4.2

We consider salaries of 45 college graduates who took a statistics course in college. Based on these data we have a sample variance of $25,150. Find 99% upper confidence bound for σ2. Let and

44,000

The distances traveled (in miles) to 7 different swim meets are given below: 12, 18, 31, 46, 69, 71, 85. Find the median distance traveled.

46 miles

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 6%?

461

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 100 statistics students generated the following 99% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within 0.04 using 95% confidence?

597

The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n= 690 drowning deaths of children with 35% of them attributable to beaches. Find the value of the test statistic z using .

6.07

According to a college survey, 15% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size 42.

6.30

The heights (in inches) of 20 adult males are listed below. 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 Find the range of the data set.

7

Let X represent the amount of time it takes a student to park in the library parking lot at the university. If we know that the distribution of parking times can be modeled using an exponential distribution with a mean of 4 minutes, find the probability that it will take a randomly selected student more than 10 minutes to park in the library lot.

d. 0.082085

An electrical firm manufactures a certain type of light bulb that has a mean light of 1,800 hours and a standard deviation of 200 hours. Find the probability that a random sample of 100 bulbs will have an average life of not more than 1775 hours and not less than 1760 hours.

d. 0.0828

At a California college, 22% of students speak Spanish, 5% speak French, and 3% speak both languages. What is the probability that a student chosen at random from the college speaks Spanish but not French?

d. 0.19

You wish to test the claim that μ > 6 at a level of significance of α = 0.05. Let sample statistics be n = 60, s = 1.4. Compute the value of the test statistic. Round your answer to two decimal places.

1.66

Find the variance of the given data. Round your answer to one more decimals than the original data. 5.0, 8.0, 4.9, 6.8 and 2.8

3.96

The probability is 0.85 that a person shopping at a certain store will spend less than $20. For random samples of 82 customers, find the mean number of shoppers who spend less than $20.

69.7

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.42 inches and a standard deviation of 0.11 inches. What percentage of bolts will have a diameter greater than 0.30 inches?

86.23%

If the standard deviation for a Poisson distribution is known to be 3, the expected value of that Poison distribution is:

9.

A group of 40 bowlers showed that their average score was 192 with a population standard deviation of 8. Assume that bowler's scores are normally distributed. Find the 95% confidence interval of the mean score of all bowlers.

(189.5, 194.5)

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.01 for a left-tailed test (H1:µ <µ0).

-2.32

(See picture) [file:2266.jpg]

-46.15

A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n =1200 subjects with 40% saying that they play a sport. Find the value of the test statistic z using

-6.928

Assume that x has a Poisson probability distribution. Find P(x = 6) when μ = 1.0.

.0005

The amount of bleach a machine pours into bottles has a mean of 28 oz. with a standard deviation of 1.05 oz. Suppose we take a random sample of 25 bottles filled by this machine. What is the standard deviation for the sample mean?

0.21

The following table shows the political affiliation of voters in one city and their positions on stronger gun control laws.

0.211

At a Ohio college, 25% of students speak Spanish, 5% speak French, and 3% speak both languages. What is the probability that a student chosen at random from the college speaks Spanish but not French?

0.22

Suppose that X has a discrete uniform distribution on the integers 20 to 79. Which of the followings are true? (i) P(X > 41) = 13/20 (ii) E(10X)= 495

Both (i) and (ii)

Construct the stem-and-leaf diagram for the below data. 16.9; 15.2; 17.5; 15.5; 16.8; 16.8; 17.1; 17.5; 15.3.

Stem Leaf 15 235 16 889 17 155

An electronic scale that displays weights to the nearest pound is used to weigh packages. The display shows only three digits. Any weight greater than the display can indicate is shown as 999. The random variable X is the displayed weight. What is the number of member in the sample space of X?

1,000

Find the test statistic t0 for a sample with n = 15, = 7, s = 0.8, and ifH1: µ < 6.0. Round your answer to three decimal places.

4.841

If two balanced die are rolled, the possible outcomes can be represented as follows. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Determine the probability that the sum of the dice is 4 or 12.

1/9

In order to efficiently bid on a contract, a contractor wants to be 99% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the standard deviation is 5 hours. How large a sample must be selected? Let z0.005 = 2.58.

42

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 50 to 60. What is the mean outcome of this experiment?

55

The grade point averages for 11 randomly selected students in a statistics class are listed below. 2.4 3.2 1.8 1.9 2.9 4.0 3.3 0.9 3.6 0.8 2.2 What is the effect on the width of the confidence interval if the sample size is increased to 15?

The width decreases.

Determine whether the given conditions justify testing a claim about a population mean μ. If so, what is formula for test statistic? The sample size is n = 49, σ = 12.3, s = 8.72and the original population is not normally distributed.

Yes, test statistic =

The Kappa lata Sigma Fraternity polled its members on the weekend party theme. The vote was as follows: six for toga, four for hayride, eight for beer bash, and two for masquerade. Display the vote count in a Pareto chart

a.

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in Vietnam revealed the following endowments (in millions of dollars) 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for the mean endowment of all private colleges in Vietnam?

a. $180.975

A student randomly selects 10 CDs at a store. The mean is $8.75 with a standard deviation of $1.50. Construct a 95% confidence interval for the population standard deviation, $$\sigma.$$ Assume the data are normally distributed.

a. ($1.03, $2.74)

A group of 40 bowlers showed that their average score was 192 with a population standard deviation of 8. Find the 95% confidence interval of the mean score of all bowlers.

a. (189.5, 194.5)

For a sample of 10 observations, you have the following information: Σxi = 253, Σyi = 172.2, Σxiyi = 643.4, Σ(xi)2 = 696, Σ(yi)2 = 152.2. What is the sample correlation coefficient between X and Y?

a. -0.93

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n = 4, x = 3, p = 1/6

a. 0.0154

A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?

a. 0.0625

According to the Center for Disease Control, 41.5% of babies born in the U.S. in 2004 were still being breastfed at 6 months of age. If 4 children who were born in the U.S. in 2004 are randomly selected, what is the probability that none of them were breastfed for at least 6 months?

a. 0.12

A multiple choice test has 10 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?

a. 0.2503

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is less than 1 year.

a. 0.254811

An archer is able to hit the bull's-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

a. 0.2627

The breakdown of workers in a particular state according to their political affiliation and type of job held is shown here. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Political Affiliation Given the worker is a Democrat, what is the probability that the worker is in a white collar job.

a. 0.526

Let Z is a standard normal variable, find P(-0.73 < Z < 2.27).

a. 0.7557

The number of monthly breakdowns of a conveyor belt at a local factory is a random variable having the Poisson distribution with λ = 2.8. Find the probability that the conveyor belt will function for a month without a breakdown. (Note: please give the answer as a real number accurate to 3 decimal places after the decimal point.)

a. 1.6

Find the standard deviation for the given probability distribution. x 0 1 2 3 4 P(x) 0.37 0.05 0.13 0.25 0.20

a. 1.60

The grade point averages for 10 randomly selected students are listed below. Construct a 90% confidence interval for the population standard deviation, $$\sigma.$$ Assume the data are normally distributed. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

b. (0.81, 1.83)

A group of 49 randomly selected students has a mean age of 22.4 years with a population standard deviation of 3.8. Construct a 98% confidence interval for the population mean.

b. (21.1, 23.7)

Suppose we have the following information from a simple regression: = 117.4, = -17.29, n = 300, = 4.3, SST = 17000, and SSE = 10000. What is the correlation coefficient?

b. -0.642

The height y and base diameter x of five tree of a certain variety produced the following data x 2 4 3 4 y 33 41 96 90 What is the value of the test statistic for testing

b. 0.026

In one city, the probability that a person will pass his or her driving test on the first attempt is 0.68. 11 people are selected at random from among those taking their driving test for the first time. What is the probability that among these 11 people, the number passing the test is between 2 and 4 inclusive?

b. 0.0308

To determine the difference , if any, between two brands of radial tires, 12 tires of each brand are tested. Assume that the lifetimes of both brands of tires come from the same normal distribution $$N(\mu, 3300^2).$$ Compute $$P(\overline{X}-\overline{Y} <-2500).$$

b. 0.0314

It has been found that 40% of the employees who complete a sequence of executive seminars go on to become vice presidents. Assume that 10 graduates of the program are randomly selected, find the probability that at least two become vice presidents. (Note: please give the answer as a real number accurate to4 decimal places after the decimal point.)

b. 0.04

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the average number of arrivals per minute?

b. 0.0667

According to a 2007 report published by the National Center on Addiction and Substance Abuse at Columbia University, 59% of teens have family dinners five or more times a week, 13% of teens have used marijuana and the proportion of teens who have family dinners 5 or more times a week or use marijuana is 0.64. What is the probability that a teen has family dinners five or more times a week and uses marijuana? Hint. Use the addition rules.

b. 0.08

The number of 113 calls in Hanoi, has a Poisson distribution with a mean of 10 calls a day. The probability of seven 113 calls in a day is

b. 0.09

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively. For the probability distribution above, find the variance. (Note: please give the answer as a real number accurate to2 decimal places after the decimal point.)

b. 0.095089

A melting point test of $$n = 10$$ samples of a binder used in manufacturing a rocket propellant resulted in $$\overline{x}=154.2^oF$$. Assume that melting point is normally distributed with $$\sigma=1.5^oF$$. What is the P-value for the testing problem $$H_0:\mu=155/ H_1 eq 155$$? Let $$P(Z<1.67)=0.952$$.

b. 0.096

The mean diameter of marbles manufactured at a particular toy factory is 0.850 cm with a standard deviation of 0.010cm. What is the probability of selecting a random sample of 100 marbles that has a mean diameter greater than 0.851 cm?

b. 0.1587

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes. Find the probability that a customer spends between 39 and 43 minutes in the supermarket.

b. 0.2120

Let $$X$$ be uniformly distributed over [0, 1]. Calculate $$E[X^3]$$.

b. 0.25

The manager of a used-car dealership is very interested in the resale price of used cars. The manager feels that the age of the car is important in determining the resale value. He collects data on the age and resale value of 15 cars and runs a regression analysis with the value of the car (in thousands of dollars) as the dependent variable and the age of the car (in years) as the independent variable. Unfortunately, he spilled his coffee on the printout and lost some of the results. The partial results left are displayed below. Multiple R 0.557 R Square "A" Adjusted R Square 0.133 Standard error "B" Observations 15000 What is the value of "A"?

b. 0.310

In 2004, the infant mortality rate (per 1,000 live births) for the 50 states and the District of Columbia had a mean of 6.98 and a standard deviation of 1.62. Assuming that the distribution is normal, what percentage of states had an infant mortality rate between 5 and 7 percent?

b. 0.39

A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). Interest rate 7.0\% 7.5\% 8.0\% 8.5\% 9.0\% Probability 0.12 0.23 0.24 0.35 0.06 $$ If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%?

b. 0.41

Let X be a random variable has the following uniform density function f(x) = 0.1 when 0< x < 10. What is the probability that the random variable X has a value greater than 5.3?

b. 0.47

A population of Australian Koala bears has a mean height of 20 inches and a standard deviation of 4 inches. You plan to choose a sample of 64 bears at random. What is the probability of a sample mean between 20 and 21.

b. 0.4772

Find the variance for the given data. Round your answer to one more decimals than original data 1, 4, -5, -9, and 6

b. 39.3

Given a sample with r = 0.833, n = 12, and = 0.05, determine the test statistic t0 necessary to test the claim ρ = 0. Round answers to three decimal places.

b. 4.761

For a group of students in a statistics class, the scatter diagram compares their test scores (y) and the number of red shirts they have(x) is shown as below. State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables.

b. Negative correlation

Construct a 98% confidence interval for the population mean, μ. Assume the population has a normal distribution. A study of 14 bowlers showed that their average score was 192 with a standard deviation of 8.

c. (186.3, 197.7)

The editor of a particular women's magazine claims that the magazine is read by 60% of the female students on a college campus. Find the probability that in a random sample of 10 female students more than two read the magazine. (Note: please give the answer as a real number accurate to4 decimal places after the decimal point.)

c. 0.0512

The probability that a tennis set will go to a tie-breaker is 17%. What is the probability that two of three sets will go to tie-breakers?

c. 0.072

Suppose that11% of people are left handed. If 6 people are selected at random, what is the probability that exactly 2 of them are left handed?

c. 0.1139

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces. Find the probability that between 15 and 18 ounces are dispensed in a cup.

c. 0.1598

Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 30 to 80. What is the probability that this experiment results in an outcome less than 40?

c. 0.2

The lengths of pregnancies are normally distributed with a mean of 264 days and a standard deviation of 25 days. If 100 women are randomly selected, find the probability that they have a mean pregnancy between 264 days and 266 days.

c. 0.2881

A polltaker asked graduating college seniors how many times they had given blood in the last year. The results of the survey are given below. The random variable x represents the number of times a person gave blood and P(x) represents the probability of selecting a graduating college who had given blood that percent of the time. What is the standard deviation for the number of times a person gave blood based on this poll? x 0 1 2 3 4 5 6 P(x) 0.30 0.25 0.20 0.12 0.07 0.04 0.02

c. 1.54

A die is rolled 10 times and the number of times that two shows on the up face is counted. If this experiment is repeated many times, find the mean for the random variable X, the number of twos thrown out of ten tosses.

c. 1.67

On a multiple choice test with 16 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the random variable X, the number of correct answers.

c. 1.732

Find the critical value or values of x2 based on the given information. H1: σ ≠ 9.3 n = 28 α = 0.05

c. 14.573, 43.194

The probability is 0.7 that a person shopping at a certain store will spend less than $20. For random samples of 28 customers, find the mean number of shoppers who spend less than $20.

c. 19.6

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 25% households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The value of the test statistic in this problem is approximately equal to

c. 2.80

Suppose you are interested in determining the relationship between the temperatures (x) on days during a summer class and the number of absences on those days (y). For a sample of 9 observations, you have the following information: Σxi = 196, Σyi = 131.7, Σxiyi = 2001.4, Σ(xi)2 = 702.3, Σ(yi)2 = 1321.5. Find the sample regression line.

c. = 9.341 + 0.243x

Which of the following is not an element of descriptive statistical problems?

c. An inference made about the population based on the sample.

Flip a coin three times, create the sample space of possible outcomes.

c. HHH HHT HTH HTT THH THT TTH TTT

A stock analyst compares the relationship between stock prices and earnings per share to help him select a stock for investment. What type of the description is?

c. Observation study

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

c. There is sufficient evidence to warrant rejection of the claim that the mean weight is at least

A Type II error is committed when

c. we don't reject a null hypothesis that is false.

A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the mean salary.

d.

The attendace counts for this season's basketball games are listed below: 227 239 215 219 221 233 229 233 235 228 245 231 Use the data to creat a sterm plot.

d.

In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6 with a population standard deviation of 5.8 hours. Find the 98% confidence interval for the population mean.

d. (17.5, 21.7)

Suppose we have the following information from a simple regression: = 107.4, = -14.39, se()= 2.8, se()= 2.4, n = 200. What is the value of the test statistic for testing H0: ?

d. -1.071

Suppose we have the following information from a simple regression: = 107.4, = -14.30, se()= 2.8, se()= 2.4, n = 200. What is the value of the test statistic for testing H0: ?

d. -5.96

Let $$\overline{X}$$ denote the sample mean of a random sample of size n1 = 16 taken from a normal distribution $$N(\mu, 36),$$ and let $$\overline{Y}$$ denote the sample mean of a random sample of size n2 = 25 taken from a different normal distribution $$N(\mu, 9).$$ Compute $$P(\overline{X} - \overline{Y}>5).$$

d. 0.001

Assume that X has a normal distribution with the mean is μ = 60.0 and the standard deviation is σ = 4.0. Find the probability that X is less than 53.0.

d. 0.0401

A group of volunteers for a clinical trial consists of 81 women and 77 men. 18 of the women and 19 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman.

d. 0.222

A normal distribution has mean μ = 60 and standard deviation = 6, find the area underthe curve to the right of 64.

d. 0.2525

According to the U.S. census, in 2005 21% of homicide victims were known to be female, 9.7% were known to be under the age of 18 and 2.8% were known to be females under the age of 18. What is the probability that a murder victim was known to be female or under the age of 18 based on these 2005 estimates?

d. 0.279

Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.

d. 0.5625 ±0 .0129

Find z if the normal curve area between 0 and z is 0.4756.

d. 1.9703

A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 99% confident that the margin of error is within 3%?

d. 1842

Find the standard deviation for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 2661; p = 0.63

d. 24.91

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 2.5 to 4.5 millimeters. What is the mean diameter of ball bearings produced in this manufacturing process?

d. 3.5 millimeters

According to a college survey, 22% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size 16.

d. 3.52

Which of the following is a continuous quantitative variable?

d. The amount of milk produced by a cow in one 24-hour period

The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of

d. descriptive statistics.

The random variable X represents the number of credit cards that adults have along with the corresponding probabilities. Find the mean and standard deviation. x 0 1 2 3 4 P(x) 0.49 0.05 0.32 0.07 0.07

d. mean: 1.18; standard deviation: 1.30

Suppose we have the following information from a simple regression: = 117.4, = -17.29, n = 300, = 4.3, SST = 17000, and SSE = 10000. What is the correlation coefficient?

e. -0.642

If two events A and B are __________, then P(A and B) = P(A)P(B).

independent

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of attended the midnight showing. The Type I error is believing that the percent of EVC students who attended is:

less than 20%, when in fact, it is at least 20%

Suppose the probability density function of the length of computer cables is from 10 to 12 millimeters. Determine the mean and standard deviation of the cable length.

mean = 11 and standard deviation = 0.58

In a pizza takeout restaurant, the following probability distribution was obtained. The random variable X represents the number of toppings for a large pizza. Find the mean and standard deviation for the random variable X. x

mean: 1.04; standard deviation: 1.09

The random variable X represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation for the random variable X. x

mean: 1.47; standard deviation: 1.19

The random variable X represents the number of credit cards that adults have along with the corresponding probabilities. Find the mean and standard deviation. x

mean: 1.62; standard deviation: 0.95

A psychologist claims that more than 3 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the given claim will be conducted. Identify the type II error for the test.

most 3 percent when it is actually more than 3 percent.

The owner of a football team claims that the average attendance at games is over 60,000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the given claim will be conducted. Identify the type II error for the test.

most 60,000, when it is actually greater than 60,000.

The time for a worker to assemble a component is normally distributed with mean 15 minutes and variance 4. Denote the mean assembly times of 16 day-shift workers and 9 night-shift workers by and , respectively. Assume that the assembly times of the workers are mutually independent. The distribution of - is

normal with mean 0 and standard deviation 5/6.

A random sample of size n = 16 is taken from a normal population with mean 40 and variance 5. The distribution of the sample mean is

normal with mean 40 and variance 5/16.

A manufacturer of electronic calculators is interested in estimating the fraction of defective units produced. A random sample of 1500 calculators contains 15 defectives. Compute a 99% upper-confidence bound on the fraction defective. Let z0.005 = 2.58 and z0.01 =2.33.

p ≤ 0.016

The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 250 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. Identify the type of data collected by PAWT.

quantitative and discrete

Given events A and B with probabilities P(A) = 0.5,P(B) = 0.4, and P(A and B) = 0.2, are A and B independent?

yes

Flip a coin three times, create the sample space of possible outcomes (H: Head, T: Tail).

HHH HHT HTH HTT THH THT TTH TTT

Suppose a 95% confidence interval for µ turns out to be (1000, 2100). Give a definition of what it means to be 95% confident in an inference

In repeated sampling, 95% of the intervals constructed would contain the population mean.

A T.V. show's executives raised the fee for commercials following a report that the show received a " No.1" rating in a survey of viewers. What type of the description is?

Observation study

What is a method of collecting data?

A retrospective study using historical data

A random sample of 10 parking meters in a beach community showed the following incomes for a day. 3.60 4.50 2.80 6.30 2.60 5.20 6.75 4.25 8.00 3.00 A simple computation yields a sample mean of 4.7 and standard deviation of 1.8. Assume the incomes are normally distributed. Find the 95% confidence interval for the true mean.

(3.41, 5.99)

A random sample of 169 students has a grade point average with a mean of 6.6 and with a population standard deviation of 0.8. Construct a 98% confidence interval for the population mean, μ.

(6.46, 6.74)

A recent study claimed that at least 15% of junior high students are overweight. In a sample of 175 students, 28 were found to be overweight. At = 0.03, determine the critical values to test the claim.

1.88

Compute the critical value that corresponds to a 94% level of confidence.

1.88

Find the critical value or values of based on the given information. H1: σ < 26.1 n = 29 = 0.01

13.565

When products and processes are designed and developed with designed experiments, they enjoy

All of the others

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the σ = 7.3 mg claimed by the manufacturer. Express the null hypothesis H 0 and the alternative hypothesis H 1 in symbolic form.

H0: σ =7.3 mg H1: σ ≠ 7.3 mg

Jared was working on a project to look at global warming and accessed an Internet site where he captured average global surface temperatures from 1866. Which of the four methods of data collection was he using?

Retrospective study

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2600 miles. What is the probability a particular tire of this brand will last longer than 57,400 miles?

a. 0.8413

Find the critical value or values of $$\chi^2$$ based on the given information. H1: σ < 0.14 n = 23 α = 0.10

a. 14.042

Determine whether the given conditions justify testing a claim about a population mean μ. If so, what is formula for test statistic? The sample size is n = 25,σ = 5.93, and the original population is normally distributed.

Yes, test statistic =

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.05 for a left-tailed test.

b. -1.645

An entomologist writes an article in a scientific journal which claims that fewer than 19 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

d. There is sufficient evidence to support the claim that the true proportion is less than 19 in ten thousand.

An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. What is the population?

d. all custormers

Given that events C and D are independent, P(C) = 0.3, and P(D) = 0.6, are C and D mutually exclusive?

no

(See picture) [file:1983.jpg]

0.135

Use the given sample data to find three quartiles: 5, 21, 13, 16, 11, 28, 36, 13, 22

12, 16, 25

Find the standard normal-curve area to the left of z = -0.54.

b. 0.2946

(See picture) [file:1982.jpg]

0

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 0.95 centimeter and a standard deviation of 0.02 centimeter. A random sample of 4 computer chips is taken. What is the variance for the sample mean?

0.0001

Let denote the sample mean of a random sample of size n1 = 16 taken from a normal distribution N(212, 36), and let denote the sample mean of a random sample of size n2 = 25 taken from a different normal distribution N(212, 9). Compute

0.001

Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 40 cards, and a sample of 3 are selected at random without replacement for functional testing. If 5 cards are defective, what is the probability that all cards in the sample are defective?

0.001

A telemarketer found that there was a 1.5% chance of a sale from his phone solicitations. Find the probability of getting 28 or more sales for 1000 telephone calls.

0.0016

If the probability of a newborn child being female is 0.5, find the probability that in 50 births, 35 or more will be female.

0.0033

In a recent survey, 85% of the community favored building a police substation in their neighborhood. If 20 citizens are chosen, what is the probability that the number favoring the substation is exactly 12?

0.0046

The Columbia Power Company experiences power failures with a mean of 0.120 per day. Use the Poisson Distribution to find the probability that there are exactly two power failures in a particular day.

0.006

Assume that the heights of men are normally distributed with a mean of 69.8 inches and a standard deviation of 2.4 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 70.8 inches.

0.0062

A study of the amount of time it take a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.5 hours and the standard deviation is 1.7 hours. If 64 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 9 hours.

0.0093

In a certain manufacturing process it is known that, on the average, 1 in every 100 items is defective. What is the probability that the fifth item inspected is the first defective item found.

0.0096

Sixty-five percent of men consider themselves knowledgeable football fans. If 15 men are randomly selected, find the probability that exactly five of them will consider themselves knowledgeable fans.

0.0096

Assume that a procedure yields a binomial distribution with a trial repeated n = 4 times. Use the binomial probability formula to find the probability of x=3 successes given the probability p=1/6 of success on a single trial.

0.0154

Car batteries produced by company A have a mean life of 3.5 years with a standard deviation of 0.4 years. A similar battery producted by company B has a mean life of 3.3 years and a standard deviation of 0.3 years. What is the probability that a random sample of 25 batteries from company A will have a mean life of at least 0.4 years more thanthe mean life of a sample of 36 batteries from company B?

0.0166

Suppose that on a particular multiple choice question, 96% of the students answered correctly. What is the probability that a randomly selected student answered the question incorrectly?

0.04

The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 25% of people with home-based computers have access to on-line services. Suppose that 10 people with home-based computers were randomly and independently sampled. What is the probability that exactly 5 of those sampled have access to on-line services at home?

0.0584

Assume that P(E) = 0.15 and P(F) = 0.48. If E and F are independent, find P(E and F).

0.072

The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.27 ounces and a standard deviation of 0.18 ounce. The cans only hold 12.51 ounces of soda. Every can that has more than 12.51 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process?

0.0912

Assume that a procedure yields a binomial distribution with a trial repeated 12 times. Use the binomial probability formula to find the probability of 5 successes given the probability 0.25 of success on a single trial.

0.103

The time between customer arrivals at a furniture store has an approximate exponential distribution with mean of 9.5 minutes. If a customer just arrived, find the probability that the next customer will not arrive for at least 21 minutes.

0.109643

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three boys in ten births.

0.172

Product codes of 1, 2 or 3 letters are equally likely. What is the mean of the number of letters in 50 codes?

100

After completing an inventory of three warehouses, a golf club shaft manufacturer described its stock of 14,542 shafts with the percentages given in the table. Suppose a shaft is selected at random from the 14,542 currently in stock, and the warehouse number and type of shaft are observed. Type of Shaft Given that the shaft is produced in warehouse 2, find the probability it has an stiff shaft.

0.344

A study of the amount of time it take a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 49 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.5 hours.

0.3487

The number of hours you spend looking at YouTube on a typical Saturday night is distributed according to the density function with . Find the probability that, on a typical Saturday night, you spend between 0.75 and 1.25 hours watching YouTube.

0.3602

Suppose that X is a continuous random variable whose probability density function is given by and for other values of What is the value of C?

0.375

A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9.75 to 11.25 gallons per minute. What is the probability that at the time the machine is checked it is pumping more than 10.65 gallons per minute?

0.40

The probability density function of the time required to complete an assembly operation is f(x)= 0.1 for 20≤ x ≤ 30 seconds. Determine the proportion of assemblies that requires more than 25 seconds to complete.

0.50

The random variable X represents the number of girls in a family of three children. Assuming that boys and girls are equally likely, find the probability that the number of girls is two or more.

0.50

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine?

0.511

A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 6%? A previous study indicates that the proportion of households with two cars is 25%.

283

The following data reflect the number of customers who test drove new cars each day for a sample of 20 days at the Redfield Ford Dealership. (See picture) Given these data, what is the interquartile range? [file:3589.jpg]

3

If you were constructing a 99% confidence interval of the population mean based on a sample of n = 12 where the standard deviation of the sample s = 3.25, the critical value of t will be

3.1058

The probability that a radish seed will germinate is 0.26. A gardener plants seeds in batches of 52. Find the standard deviation for the random variable X, the number of seeds germinating in each batch.

3.16

A die is rolled 80 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.

3.33

Find the test statistic t0 for a sample with n = 12, = 30.2, s = 2.2, and α = 0.01 if H0 : µ = 28. Round your answer to three decimal places.

3.464

(See picture) [file:1979.jpg]

0.61

Let X be a uniform random variable over the interval [1, 9] . What is the probability that the random variable X has a value less than 6?

0.625

Find the variance of the following probability distribution. x

3.57

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 2.55 to 4.75 millimeters. What is the mean diameter of ball bearings produced in this manufacturing process?

3.65 millimeters

A die is rolled 22 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

3.67

Assume that X is normally distributed with a mean of 23 and a standard deviation of 5. Find the value of c if P(X > c) = 0.0592.

30.81

For a standard normal distribution, find the percentage of data that are more than 1 standard deviation away from the mean.

31.74%

A Professor at Hanoi Medical University is interested in estimating the birth weight of infants. How large a sample must he select if he desires to be 99% confident that the true mean is within 0.1 kilograms of the sample mean? A past experience indicates that the standard deviation of the birth weights is known to be 0.7 kilograms. Let z0.005 = 2.58.

327

Use the given sample data to find three quartiles: 15, 21, 3, 6, 10, 28, 36, 1

4.5, 12.5, 24.5

Assume that X has a normal distribution with the mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is between 14.3 and 16.1.

0.6826

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 43.2 minutes and a standard deviation of 5.2 minutes. Find the probability that a customer spends less than 46.5 minutes in the supermarket.

0.7180

Let Z is a standard normal variable, find P(-0.73 < Z < 2.27).

0.7557

The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height. Round your answer to one decimal place.

76.4

For a standard normal distribution, find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean.

84.00%

A large retail company gives an employment screening test to all prospective employees. Frankin Gilman recently took the test and it was reported back to him that his score placed him at the 80th percentile. Therefore:

Frankin scored as high or higher than 80 percent of the people who took the test.

The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 20% of people with home-based computers have access to on-line services. Suppose that 15 people with home-based computers were randomly and independently sampled. What is the probability that exactly 5 of those sampled have access to on-line services at home?

b. 0.1032

The probability of winning a certain lottery is 1/51949. For people who play 560 times, find the standard deviation for the random variable X, the number of wins.

b. 0.1038

The table below shows the times (in hours) that seven students spend watching television and using the Internet. Construct a scatter diagram for the data and state whether these times have no correlation, a positive correlation, or a negative correlation.

c. Positive correlation

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. Claim: μ = 119. Sample data: n = 15, $$\overline{x} = 103,$$ s = 15.2. The sample data appear to come from a normally distributed population with unknown μ and

c. Student t

A basketball player is asked to shot free throws in sets of four. The player shoots 100 sets of 4 free throws. The probability distribution for making a particular number of free throws id given below. Determine the standard deviation for this discrete probability distribution. x 0 1 2 3 4 P(x) 0.02 0.07 0.22 0.27 0.42

b. 1.05

A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9.5 to 13.5 gallons per minute. Find the variance of the distribution.

b. 1.33

Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected?

b. 1.96%

Suppose we have the following information from a simple regression: n = 15, = 301.5, = 385.7, = 1719.8, = 1200.9, = 1090.5. What is the y-intercept of the regression line of hours on income?

b. 12.97

A simple regression model has the form: = 10 + 2x. As x increases by one unit, then the value of y will increase by:

b. 2 units

You want to explore the relationship between the grades students receive on their first two exams. For a sample of 17 students, you find a correlation coefficient of 0.47. What is the value of the test statistic for testing H0: ρ = 0 vs. H1: ρ 0 ?

b. 2.06

If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample s = 0.05, the critical value of t will be

b. 2.7969.

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below: 95, 38, 221, 122, 258, 237, 233. Find the median number of newspapers sold

b. 221

A study of the checkout times of 100 customers at a supermarket resulted in the distribution below. Find the mean and standard deviation. x(minutes) f 0.5-1.5 15 1.5-2.5 20 2.5-3.5 15 3.5-4.5 20 4.5-5.5 30

b. 3.3 and 1.4599

Given the equation of a regression line is = 4x - 6, what is the best predicted value for y given x = 9? Assume that the variables x and y have a significant correlation.

b. 30

Find the percentile for the data point. data set: 3 11 8 6 3 3 11 6 3 11 2 11 15 4 9 3 12 8 6 11 data point: 6

b. 35

Find the mean for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 33; p = 0.2

b. 6.6

In simple linear regression, which of the following statements indicates there is no linear relationship between the variables x and y?

b. Coefficient of correlation is 0.0.

Find z if the normal curve area to the right of z is 0.8997.

c. -1.2798

A sample of 8 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 1720.875, = 1150, = 1090.5. What is the slope of the regression line of hours on income?

c. 0.6337

A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%?

a. 1068

The probability that an individual is left-handed is 0.15. In a class of 93 students, what is the probability of finding five left-handers?

d. 0.002

Assume that the heights of men are normally distributed with a mean of 69.8 inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 70.8 inches.

d. 0.0021

A tennis player makes a successful first serve 59% of the time. If she serves 7 times, what is the probability that she gets exactly3 first serves in? Assume that each serve is independent of the others.

d. 0.2031

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 years or more.

d. 0.229790

The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Hanoi. X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05 The probability of more than 2 accidents is

d. 0.25

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. Let $$P(Z<-0.62) =0.2674;P(Z<-0.5) = 0.3085; P(Z<-0.37)=0.3551;P(Z<-0.87)=0.1915$$.

d. 0.3085

Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. Test 1 7.5 6.4 6.6 5.8 8.3 Test 2 6.7 6.6 7.2 4.0 6.7 Find the value of the linear correlation coefficient r.

d. 0.58

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 95% confidence interval to estimate the true proportion of students on financial aid.

d. 0.59 ± 0.068

The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Hours 5 10 4 6 10 9 Score 4 8 3 6 9 8 $$ Find the value of the linear correlation coefficient $$r$$.

d. 0.973

The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Use the regression equation to predict the life span, y, for a gestation period of 6 months, x. Assume the variables x and y have a significant correlation. Gestation, x 8 2.1 3.8 Life span, y 30 12 10

d. 21.97

If a sample of n = 40 people is selected and the sample correlation between two variables is r = 0.468, what is the test statistic value for testing whether the true population correlation coefficient is equal to zero?

d. 3.26

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the Manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month. Miles traveled, x 4 8 10 Sales, y 27 58 61 Calculate the test statistic to test the claim ρ = 0. Round answers to three decimal places.

d. 3.857

The distances traveled (in miles) to 7 different swim meets are given below: 12, 18, 31, 46, 69, 71, 85. Find the median distance traveled.

d. 46 miles

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 6%?

d. 461

Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid between $148,800 and $151,200 if the standard deviation is $1200.

d. 68%

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg?

d. 95%

Suppose you are interested in determining the relationship between the temperatures (x) on days during a summer class and the number of absences on those days (y). For a sample of 9 observations, you have the following information: Σxi = 196, Σyi = 131.7, Σxiyi = 2001.4, Σ(xi)2 = 702.3, Σ(yi)2 = 1321.5. Find the sample regression line.

d. = 9.341 + 0.243x

The table below shows the legal costs and the profits of a company from 2000 to 2005. Construct a scatter diagram for the data and state whether legal costs and profits for this company have no correlation, a positive correlation, or a negative correlation for this period.

d. Negative correlation

Which of the following statements is false i) If X1, X2,...,Xn is a random sample of size n,the sample standard deviation S is nota statistic. ii) The probability distribution of a statistic is called a sampling distribution. iii) A statistic is any function of the observations in a random sample. iv) The sampling distribution of a statistic does not depend on the distribution of the population.

i) and iv)

Assume that P(A) = 0.7 and P(B) = 0.2. If A and B are independent, find P(A and B).

0.14

Find the mean of the data summarized in the given frequency distribution. Daily Low Temperature (F)

53.4

A stem-and-leaf diagram for a set of examination scores is given below. Find sample median of these data. Stem

55.5

Find the standard deviation for the given sample data: 2 6 2 2 1 4 4 2 4 2 3 8 4 2 2 7 7 2 3 11

a. 2.6

Suppose that a random sample of 10,000 (X, Y) pairs yielded: = 10.4, se()= 21.2, se()= 2.4. What is the value of the test statistic for testing H0: ?

d. 0.019

Find the critical value or values of x2 based on the given information. H0: σ = 8.0 n = 10 α = 0.01

d. 1.735, 23.589

Find the mode(s) for the given dample data 98, 25, 98, 13, 25, 29, 56, 98

d. 98

Suppose that 14% of people are left handed. If 5 people are selected at random, what is the probability that exactly 2 of them are left handed?

0.1247

An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. What is the sample?

three selected custermers

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E.

2, 4, 6, 8, 10

The Columbia Power Company experiences power failures with a mean of 0.210 per day. Use the Poisson Distribution to find the probability that there are exactly two power failures in a particular day.

a. 0.018

According to police sources a car with a certain protection system will be recovered 87% of the time. Find the probability that 4 of 7 stolen cars will be recovered.

a. 0.044

Use the given information to find the P-value. The test statistic in a two-tailed test is z = -1.63.

a. 0.1032

Given the supply of a commodity, x, and the price of a commodity, y, would you expect a positive correlation, a negative correlation, or no correlation?

c. negative correlation

Given the size of a human's brain, x, and their score on an IQ test, y, would you expect a positive correlation, a negative correlation, or no correlation?

c. no correlation

Let $$\overline{X}$$ denote the sample mean of a random sample of size n1 = 16 taken from a normal distribution N(m, 36), and let $$\overline{Y}$$ denote the sample mean of a random sample of size n2 = 25 taken from a different normal distribution $$N(\mu, 9).$$ The distribution of $$\overline{X}$$ - $$\overline{Y}$$ is

c. normal with mean 0 and standard deviation 1.6155

Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 130 students and carefully recorded their parking times. Identify the sample of interest to the university administration.

c. parking times of the 130 students

Assume that you are predicting X from Y. Which of the following correlation coefficients would yield predictions with the most error?

c. r = 0.14

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.1 for a two-tailed test.

c. ±1.645

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. α = 0.05 for a two-tailed test.

c. ±1.96

Given events E and F with probabilities P(E) = 0.65 and P(F) = 0.19, are E and F mutually exclusive?

cannot be determined

The manager of a movie theater has determined that the distribution of customers arriving at the concession stand is Poisson distributed with a standard deviation equal to 2 people per 10 minutes. If the servers can accommodate 3 customers in a 10-minute period, what is the probability that the servers will be idle for an entire ten minute period?

0.0183

The lengths of human pregnancies are normally distributed with a mean of 269 days and a standard deviation of 16 days. What is the probability that a pregnancy lasts at least 302 days?

0.0196

The thickness measurements of a coating process are uniform distributed with values 0.1, 0.14, 0.18, 0.16. Determine the standard deviation of the coating thickness for this process.

0.03

Let X represent the amount of time it takes a student to park in the library parking lot at the university. If we know that the distribution of parking times can be modeled using an exponential distribution with a mean of 4 minutes, find the probability that it will take a randomly selected student more than 10 minutes to park in the library lot.

0.082085

An archer is able to hit the bull's-eye 57% of the time. If she shoots 15 arrows, what is the probability that she gets exactly 6 bull's-eyes? Assume each shot is independent of the others.

0.0863

Let X represent the amount of time it takes a student to park in the library parking lot at the university. If we know that the distribution of parking times can be modeled using an exponential distribution with a mean of 4.8 minutes, find the probability that it will take a randomly selected student more than 9 minutes to park in the library lot.

0.153355

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 13.5 ounces and a standard deviation of 3.5 ounces. Find the probability that between 13 and 14.4 ounces are dispensed in a cup.

0.1583

Assume that X has a normal distribution with the mean is µ= 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 16.1

0.1587

Find the probability that in 20 tosses of a fair six-sided die, a five will be obtained at least 5 times.

0.2313

According to the U.S. census, in 2005 25% of homicide victims were known to be female, 8.7% were known to be under the age of 18 and 2.7% were known to be females under the age of 18. What is the probability that a murder victim was known to be female or under the age of 18 based on these 2005 estimates?

0.310

In one region, the September energy consumption levels for single-family homes are normally distributed with a mean of 1155 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1050 kWh and 1225 kWh.

0.3109

If X is a normal random variable with μ = 50 and σ = 6, then the probability that X is not between 44 and 56 is

0.3174.

A group of volunteers for a clinical trial consists of 88 women and 77 men. 28 of the women and 39 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman.

0.318

In one city, the probability that a person will pass his or her driving test on the first attempt is 0.59. 23 people are selected at random from among those taking their driving test for the first time. What is the probability that among these 23 people, the number passing the test is between 15 and 18 inclusive?

0.3362

A bin contains 15 defective (that immediately fail when put in use), 20 partially defective (that fail after a couple of hours of use), and 30 acceptable transistors. A transistor is chosen at random from the bin and put into use. If it does not immediately fail, what is the probability it is acceptable?

0.60

According to a survey of American households, the probability that the residents own 3 cars if annual household income is over $25,500 is 83%. Of the households surveyed, 62% had incomes over $25,500 and 84% had 3 cars. The probability that annual household income is over $25,500 if the residents of a household own 3 cars is:

0.61

Let X be a uniform random variable over the interval [0, 8] . What is the probability that the random variable X has a value greater than 3?

0.625

(See picture) [file:3690.jpg]

0.948

A polltaker asked graduating college seniors how many times they had given blood in the last year. The results of the survey are given in the table. The random variable X represents the number of times a person gave blood and P(x) represents the probability of selecting a graduating college who had given blood that percent of the time. What is the standard deviation for the number of times a person gave blood based on this poll? [file:1911.jpg]

1.16

Let X be a continuous random variable with probability density function defined by Find the mean of X

1/2

Ten cartons of fragile ceramic castings were shipped on each of two air freight carries. On delivery at their destination the cartons were opened and inspected. The number of damaged items per carton were as follows: 17, 20, 1, 18, 5, 14, 18, 10, 6, 2. Assume that you are finding the frequency distribution using groupings: 1-4 inclusively, 5-8 inclusively, 9-12 inclusively and so on.What is the frequency of the interval 5-8?

2

The quality control manager for a filling operation in a bottling plant is concerned with the variability in the volume of milk dispensed into gallon jugs. The filling process results in jugs whose volumes are normally distributed with a mean of 1.02 gallons. The process standard deviation should be less than 0.004 gallons. A sample of 35 jugs was selected and the sample standard deviation was determined to be 0.0036 gallons. What is the value of test statistic for the test H1: < 0.004

27.54

Find the critical value or values of based on the given information. H1: σ > 9.3 n = 18 = 0.05

27.587

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 30 minutes and a standard deviation of 6 minutes. A random sample of 25 cars is selected. So, 90% of the sample means will be greater than what value?

28.5 minutes

Find the critical value or values of based on the given information. H1: σ > 4.5 n = 19 = 0.05

28.869

(See picture) [file:2259.jpg]

29.07

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 6%? [file:2241.jpg]

461

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 14 ounces and a standard deviation of 4.2 ounces. Find the number of ounces above which 98% of the dispensed sodas will fall.

5.4

Use the given sample data to find Q1. 55, 52, 52, 52, 49, 74, 67, 55.

52.0

If a manager believes that the required sample size is too large for a situation in which she desires to estimate the mean income of blue collar workers in a state, which of the following would lead to a reduction in sample size?

All of the above.

Which of the following is an acceptable format for setting up class boundaries for a frequency distribution?

All of the other choices is correct

For each of the following pairs of events, which are subsets of the set of all possible outcomes when a coin is tossed three times, choose the pair(s) is (are) independent.

All of the others

A psychologist claims that more than 16 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

H0: p =16% H1: p >16%

A cereal company claims that the mean weight of the cereal in its packets is at least 14.4 oz. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

H0: μ = 14.4 H1: μ >14.4

Carter Motor Company claims that its new sedan, the Libra, will average better than 70 miles per gallon in the city. Use μ, the true average mileage of the Libra. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

H0: μ = 70 H1: μ >70

Both Nualart and Tom have a bag of candy containing a lollipop (LP), a cherry drop (CD), and a lemon drop (LD). Each takes out a piece and eats it. What are the possible pairs of candies eaten? Create the sample space of possible outcomes.

LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD

A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 200 statistics students generated the following 90% confidence interval: (0.48, 0.64). Based on the interval above, is the population proportion of females equal to 0.60?

Maybe. 0.60 is a believable value of the population proportion based on the information above.

A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?

Maybe. 0.60 is a believable value of the population proportion based on the information above.

Find the mean of the data summarized in the given frequency distribution. Daily Low Temperature (F) Frequency 35-39 1 40-44 3 45-49 5 50-54 11 55-59 7 60-64 7 65-69 1

b. 53.4

A stock analyst compares the relationship between stock prices and earnings per share to help him select a stock for investment. What type of the description is?

Observation study

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviationless thanthe σ = 7.3 mg claimed by the manufacturer. Assume that a hypothesis test of the given claim will be conducted. Identify the type II error for the test.

The error of failing to reject the claim that the standard deviation is at least 7.3 mg when it is actually less than 7.3 mg.

Which of the following is a discrete quantitative variable?

The number of cracks exceeding one-half inch in 10 miles of an interstate highway.

The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of 2.3 years. Construct the 98% confidence interval for the population variance. Assume the data are normally distributed. Let $$\chi^2_{0.01,11}=24.72;\chi^2_{0.99,11}=3.05$$.

a. (2.4, 19.1)

For sample size 16, the sampling distribution of the sample mean will be approximately normally distributed...

if the shape of the population is normally distributed.

For sample size 1, the sampling distribution of the mean will be normally distributed

only if the population is normally distributed.

For sample sizes greater than 40, the sampling distribution of the mean will be approximately normally distributed.

regardless of the shape of the population.

The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment?

{0, 1, 2}

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is odd. List the sample points in E.

{1, 3, 5, 7, 9}

Using Excel to find three quartiles for the given data below: 1, 3, 6, 10, 15, 21, 28, 36.

b. 5.25, 12.5, 22.75

The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of 2.7 years. Construct the 98% confidence interval for the population variance, $$\sigma^2.$$ Assume the data are normally distributed

a. (3.2, 26.3)

A random sample of 60 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 15 of these helmets some damage was observed. Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test.

(0.14, 0.36)

[file:3649.jpg]

(ii)

The probability that an individual is left-handed is 0.15. In a class of 30 students, what is the probability of finding five left-handers?

0.186

The world's smallest mammal is the bumblebee bat. Such bats are roughly the size of a large bumblebee. A sample of the weights for 5 randomly selected bats has standard deviation of 0.33. Assume that the weights of the bats are normally distributed. Construct a 98% lower confidence bound for the standard deviation of weights for all such bats. Let and

0.193

If a random variable has the normal distribution with μ = 30 and σ = 5, find the probability that it will take on the value between 31 and 35.

0.262

A data processing firm sampled 75 small businesses to find the number of days their computer systems were down during the previous three months. The distribution of responses is given below. Find the sample mean. Days of down time

2.2

Suppose a 99% confidence interval for population mean turns out to be (1500, 2200). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?

Both increase the sample size and decrease the confidence level.

The principal of a middle school claims that test scores of the seventh-graders at her school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by σ = 17.4. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

H0: σ = 17.4 H1: σ < 17.4

A researcher claims that 26% of voters favor gun control.Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

H0:p = 0.26 H1: p ≠ 0.26

Flip a coin twice, create the sample space of possible outcomes. (Below, H stands for Head, T stands for Tail)

HH HT TH TT

Product codes of 6, 7, 8 or 9 letters are equally likely. Which of the following statements are true? (i) Standard deviation of the number of letters in one code is 1.25. (ii) The probability of the event that the code has at least 7 letters is 0.5

None of the other choices is correct

A manager wishes to estimate the proportion of parts in his inventory that are in proper working order. However, the sample size that he has been informed he will need exceeds his budget. Which of the following steps might he take to reduce the required sample size?

None of the others.

Two white sheep mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene dominates. List the possible outcomes. W = white and B = black.

WW, BW

The height y and base diameter x of five tree of a certain variety produced the following data x 1 2 2 5 y 30 40 90 120 Find the equation of the estimated regression line of y on x.

a. = 21.11x+17.22

In a simple linear model, testing H0 : = 0 is the same as testing:

a. H0: β1 = 0

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 50°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

c. The error of rejecting the claim that the mean temperature equals 50°F when it really does equal 50°F.

Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called

c. descriptive statistics.

The width of a confidence interval estimate for a proportion will be

c. narrower for 90% confidence than for 95% confidence.

Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 130 students and carefully recorded their parking times. Identify the sample of interest to the university administration.

parking times of the 130 students

For sample sizes greater than 40, the sampling distribution of the mean will be approximately normally distributed...

regardless of the shape of the population.

For sample sizes greater than 50, the sampling distribution of the mean will be approximately normally distributed

regardless of the shape of the population.

For a standard normal distribution, find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean.

d. 84.00%

Which of the following is not true about the standard normal distribution?

b. The area under the standard normal curve to the left of z = 0 is negative.

(See picture) [file:2268.jpg]

(i)

Let the random variable X have a discrete uniform distribution on the interval [1, 35]. Determine the mean and variance of X.

18 and 102

Find the sample standard deviation. 15 42 53

19.6

Product codes of 6, 7, 8 or 9 letters are equally likely. Which of the following statements are true? (i) Standard deviation of the number of letters in one code is 1.19. (ii) The probability of the event that the code has at least 7 letters is 0.5

(i) only

Suppose that X has a discrete uniform distribution on the integers 2 to 8. Which of the following are true? (i) E(4X) = 20 (ii) σ(X) = 4

(i) only

Suppose that a qualitative variable has three categories with frequencies of occurrence shown in the table. When constructing a pie chart, what is the size of the angle for class A? [file:3558.jpg]

(ii)

(See picture) [file:2245.jpg]

(iii)

(See picture) [file:2264.jpg]

(iii)

(See picture) [file:2112.jpg]

(iv)

(See picture) [file:2246.jpg]

(iv)

(See picture) [file:2271.jpg]

(iv)

Find the test statistic t0 for a sample with n = 17, = 17.7, s = 2.4, and if H1: μ ≠ 17.9. Round your answer to three decimal places.

-0.344

An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 549 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 99% confidence level.

(0.318, 0.422)

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 95% confidence interval to estimate the true proportion of students on financial aid.

(0.522, 0.658)

Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.

(0.5496, 0.5754)

A sample of the grade point averages for 10 randomly selected students has mean of 6.7 and standard deviation of 1.0. Construct a 90% confidence interval for the population standard deviation, Assume the data are normally distributed.

(0.73, 1.65)

The grade point averages for 10 randomly selected high school students are listed below and has mean of 2.54 and standard deviation of 1.11. 2.9 0.9 4.0 3.6 0.8 2.0 3.2 1.8 3.3 2.9 Assume the grade point averages are normally distributed. Find a 98% confidence interval for the true mean.

(1.55, 3.53)

In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6 with a population standard deviation of 5.8 hours. Find the 98% confidence interval for the population mean. [file:2188.jpg]

(17.5, 21.7)

Construct a 99% confidence interval for the population mean, μ. Assume the population has a normal distribution. A group of 29 randomly selected students has a mean age of 20.4 years with a standard deviation of 3.5 years.

(18.6, 22.2)

Construct a 96% confidence interval for the population mean, μ. Assume the population has a normal distribution. A study of 31 bowlers showed that their average score was 187 with a standard deviation of 8.

(183.9, 190.1)

A group of 55 bowlers showed that their average score was 190 with a population standard deviation of 8. Find the 99% confidence interval of the mean score of all bowlers.

(187.2, 192.8)

A group of 40 bowlers showed that their average score was 192 with a population standard deviation of 8. Assume that bowler's scores are normally distributed. Find the 95% confidence interval of the mean score of all bowlers. [file:2195.jpg]

(189.5, 194.5)

Assume that the heights of men are normally distributed. A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of 3.2 inches. Construct a 99% confidence interval for the population standard deviation, (sigma). [file:2224.jpg]

(2.2, 5.8)

A random sample of 15 students has a grade point average of 2.86 with a standard deviation of 0.78. Construct the confidence interval for the population mean at a significant level of 10% . Assume the population has a normal distribution.

(2.51, 3.21)

A random sample of 10 parking meters in a beach community showed the following incomes for a day. 3.60 4.50 2.80 6.30 2.60 5.20 6.75 4.25 8.00 3.00 A simple computation yields a sample mean of 4.7 and standard deviation of 1.8. Assume the incomes are normally distributed. Find the 95% confidence interval for the true mean. [file:2201.jpg]

(3.41, 5.99)

In a sample of 25 randomly selected women, it was found that their mean height was 65.2 inches. From previous studies, it is assumed that the standard deviation, is 2.4. Construct the 95% confidence interval for the population mean.

(64.3, 66.1)

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A random sample of 24 fluorescent light bulbs has a mean life of 665 hours with a standard deviation of 24 hours.

(654.9, 675.1)

Construct a 95% confidence interval for the population standard deviation of a random sample of 15 men who have a mean weight of 165.2 pounds with a standard deviation of 10.3 pounds. Assume the population is normally distributed. [file:2225.jpg]

(7.5, 16.2)

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 28 randomly selected students has a mean test score of 82.5 with a standard deviation of 9.2.

(78.93, 86.07)

Construct a 95% confidence interval for the population standard deviation σ of a random sample of 25 men who have a mean weight of 170.4 pounds with a standard deviation of 10.3 pounds. Assume the population is normally distributed.

(8.0, 14.3)

A recent study claimed that at least 17% of junior high students are overweight. In a sample of 175 students, 28 were found to be overweight. At = 0.01, determine the value of the test statistic to test the claim.

-0.35

Find z if the normal curve area to the right of z is 0.8997.

-1.2798

A telephone company claims that 25% of its customers have at least two telephone lines. The company selects a random sample of 500 customers and finds that 108 have two or more telephone lines. At = 0.05, compute the value of the test statistic to test the company's claim.

-1.76

You wish to test the claim that μ ≠ 17 at a level of significance of α = 0.05 and sample statistics are given n = 36, s = 2.5, . Compute the value of the test statistic. Round your answer to two decimal places.

-2.16

An automobile service center can take care of 12 cars per hour. If cars arrive at the center randomly and independently at a rate of 8 per hour on average, what is the probability of the service center being totally empty in a given hour?

0.0003

The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 4.3. Based on this, the probability that 2 containers will contain less than 2 defects is:

0.0018

In a recent survey, 95% of the community favored building a police substation in their neighborhood. If 50 citizens are chosen, what is the probability that the number favoring the substation is exactly 42?

0.0024

Samples of 10 parts from a metal punching process are selected every hour. Let X denote the number of parts in the sample of 10 that require rework. If the percentage of parts that require rework at 3%, what is the probability that X exceeds 2?

0.0028

According to police sources a car with a certain protection system will be recovered 78% of the time. Find the probability that 3 of 8 stolen cars will be recovered.

0.0137

To determine the difference , if any, between two brands of radial tires, 12 tires of each brand are tested. Assume that the lifetimes of both brands of tires come from the same normal distribution N(12500, 33002). Compute

0.0314

The time for a worker to assemble a component is normally distributed with mean 15 minutes and variance 4. Denote the mean assembly times of 16 day-shift workers and 9 night-shift workers by and , respectively. Assume that the assembly times of the workers are mutually independent. Compute P( - < -1.5) is

0.0359

Assume that X has a normal distribution with the mean is μ = 60.0 and the standard deviation is σ = 4.0. Find the probability that X is less than 53.0.

0.0401

Patients arriving at an outpatient clinic follow an exponential distribution with mean 22 minutes. What is the average number of arrivals per minute?

0.0455

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $20,000 is 90%. Of the households surveyed, 60% had incomes over $20,000 and 60% had 2 cars. The probability that the residents of a household own 2 cars and have an income less than or equal to $20,000 a year is:

0.06

The probability is 5% that an electrical connector that is kept dry fails during the warranty period of a portable computer. If the connector is ever wet, the probability of a failure during the warranty period is 20%. If 90% of the connectors are kept dry and 10% are wet, what proportion of connectors fail during the warranty period?

0.065

A multiple choice test has 22 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 8 questions correctly?

0.0869

A machine pours beer into 16 oz. bottles. Experience has shown that the number of ounces poured is normally distributed with a standard deviation of 1.2 ounces. Find the probabilities that the amount of beer the machine will pour into the next bottle will be between 12.5 and 14.5 ounces.

0.1039

Fifty percent of the people that get mail-order catalogs order something. Find the probability that only three of 10 people getting these catalogs will order something.

0.117

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at least 40 times.

0.1210

Sixty percent of the people that get mail-order catalogs order something. Find the probability that only three of 8 people getting these catalogs will order something.

0.124

A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $705 per month and a standard deviation of $48 per month. Refer to such expenses as PCE's (personal call expenses). Find the probability that a randomly selected month had a PCE that falls below $650.

0.1259

Forty percent of babies born in the U.S. in 2004 were still being breastfed at 6 months of age. If 4 children who were born in the U.S. in 2004 are randomly selected, what is the probability that none of them were breastfed for at least 6 months?

0.1296

Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 30 to 80. What is the probability that this experiment results in an outcome less than 45?

0.30

At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-state have passed the ELM. If a randomly selected student has passed the ELM, the probability the student is from out-of-state is ________.

0.136

The number of customers that arrive at a fast-food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. What is the probability that exactly 8 customers will arrive in a one-hour period?

0.1366

An electrical firm manufactures a certain type of light bulb that has a mean light of 1,850 hours and a standard deviation of 190 hours. Find the probability that a random sample of 100 bulbs will have an average life of more than 1,870 hours.

0.1463

According to a 2007 report published by the Columbia University, 69% of teens have family dinners five or more times a week, 11% of teens have used marijuana and the proportion of teens who have family dinners 5 or more times a week or use marijuana is 0.65. What is the probability that a teen has family dinners five or more times a week and uses marijuana? Hint. Use the addition rules.

0.15

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $35,000 is 70%. Of the households surveyed, 50% had incomes over $35,000 and 80% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $35,000 a year is:

0.15

The amount of corn chips dispensed into a 20-ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 20.5 ounces and a standard deviation of 0.5-ounce. Suppose 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags exceeded 20.55 ounces.

0.1587

The area to the right of z = 1.0 is equal to

0.1587.

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.5 years. Find the probability that the time until the first critical-part failure is 6 years or more.

0.180092

At a California college, 22% of students speak Spanish, 5% speak French, and 3% speak both languages. What is the probability that a student chosen at random from the college speaks Spanish but not French?

0.19

If the amount of gasoline purchased per car at a large service station has a population mean of $34 and a population standard deviation of $2 and a random sample of 100 cars is selected, find the value of the standard deviation of the sample mean.

0.2

A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9.25 to 12.25 gallons per minute. Find the probability that between 10.5 gallons and 11.15 gallons are pumped during a randomly selected minute.

0.217

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income less than or equal to $25,000 a year is:

0.22

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 13 ounces and a standard deviation of 2.5 ounces. Find the probability that more than 14.8 ounces is dispensed in a cup.

0.2358

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is less than 1 year.

0.254811

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.2 years. Find the probability that the time until the first critical-part failure is less than 1 year.

0.268384

According to the U.S. census, in 2005, 21% of homicide victims were known to be female, 9.7% were known to be under the age of 18 and 2.8% were known to be females under the age of 18. What is the probability that a murder victim was known to be female or under the age of 18 based on these 2005 estimates?

0.279

Ms. Anne figures that there is a 40% chance that her company will set up a branch office in Ohio. If it does, she is 70% certain that she will be made manager of this new operation. What is the probability that Anne will be a Ohio branch office manager?

0.28

In 2004, the infant mortality rate (per 1,000 live births) for the 50 states and the District of Columbia had a mean of 6.98 and a standard deviation of 1.62. Assuming that the distribution is normal, what percentage of states had an infant mortality rate between 5.6 and 7.1 percent?

0.3324

A machine pours beer into 16 oz. bottles. Experience has shown that the number of ounces poured is normally distributed with a standard deviation of 1.5 ounces. Find the probabilities that the amount of beer the machine will pour into the next bottle will be more than 16.5 ounces.

0.3385

A basketball player has made 70% of his foul shots during the season. If he shoots 3 foul shots in tonight's game, what is the probability that he makes all of the shots?

0.343

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $30,000 is 70%. Of the households surveyed, 50% had incomes over $30,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income over $30,000 a year is:

0.35

The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 10 minutes and a standard deviation of 2.1 minute. Find the probability that a randomly selected college student will take between 8.5 and 10.5 minutes to find a parking spot in the library lot.

0.3566

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 2.8 minutes. What proportion of callers is put on hold longer than 2.8 minutes?

0.367879

It was found that 60% of the workers were white, 30% were black and 10% are other races. Given that a worker was white, the probability that the worker had claimed bias was 30%. Given that a worker was black, the probability that the worker had claimed bias was 40%. Given that a worker was other race, the probability that the worker had claimed bias was 0%. If a randomly selected worker had claimed bias, what is the probability that the worker is black?

0.4

The age (in years) of randomly chosen T-shirts in your wardrobe from last summer is distributed according to the density function with . Find the probability that a randomly chosen T-shirt is between 2 and 8 years old

0.417

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3.3 minutes. What proportion of callers is put on hold longer than 2.8 minutes?

0.42806

LetZ is a standard normal variable, find theprobability that Z lies between -2.41 and 0.

0.4920

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most two boys in five births.

0.500

The breakdown of workers in a particular state according to their political affiliation and type of job held is shown here. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Political Affiliation Given the worker is a Democrat, what is the probability that the worker is in a white collar job.

0.526

Mr. Ômô figures that there is a 65% chance that his university will set up a branch office in Lao Cai. If it does, he is 90% certain that she will be made director of this new branch. What is the probability that Ômô will be a Lao Cai branch office director?

0.585

(See picture) [file:2228.jpg]

0.59 ± 0.068

It was found that 60% of the workers were white, 30% were black and 10% are other races. Given that a worker was white, the probability that the worker had claimed bias was 30%. Given that a worker was black, the probability that the worker had claimed bias was 40%. Given that a worker was other race, the probability that the worker had claimed bias was 0%. If a randomly selected worker had claimed bias, what is the probability that the worker is white?

0.6

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 4.2 minutes. What proportion of customers having to hold more than 1.8 minutes will hang up before placing an order?

0.65144

If a random variable has the normal distribution with μ = 30 and σ = 5, find the probability that it will take on the value less than 32.

0.6554

An airline reports that it has been experiencing a 12% rate of no-shows on advanced reservations. Among 100 advanced reservations, find the probability that there will be fewer than 15 no-shows.

0.7840

In Orange County, 51% of the adults are males. One adult is randomly selected for a survey involving credit card usage. It is later learned that the selected survey subject was smoking a cigar. Also, 7.5% of males smoke cigars, whereas 1.9% of females smoke cigars. Use this additional information to find the probability that the selected subject is a male.

0.804

The weekly salaries of elementary school teachers in one state are normally distributed with a mean of $595 and a standard deviation of $43. What is the probability that a randomly selected elementary school teacher earns more than $555 a week?

0.8239

A test consists of 10 true/false questions. To pass the test a student must answer at least 4 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

0.8281

A research group asked the students if they carry a credit card. The responses are listed in the table. If a student is randomly selected, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places.

0.833

A basketball player has made 95% of his foul shots during the season. If he shoots 3 foul shots in tonight's game, what is the probability that he makes all of the shots?

0.857

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be less than 8 minutes?

0.8647

The probability that a student at a certain college is male is 0.55. The probability that a student at that college has a job off campus is 0.67. The probability that a student at the college is male and has a job off campus is 0.35. If a student is chosen at random from the college, what is the probability that the student is male or has an off campus job?

0.87

A salesperson knows that 20% of her presentations result in sales. Find the probabilities that in the next 60 presentations at least 9 result in sales.

0.8732

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?

0.8767

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(0.2 < Z < a) = 0.2314, find a.

0.8805

A greenhouse is offering a sale on tulip bulbs because they have inadvertently mixed pink bulbs with red bulbs. If 35% of the bulbs are pink and 65% are red, what is the probability that at least one of the bulbs will be pink if 5 bulbs are purchased?

0.8840

According to a survey of American households, the probability that the residents own 3 cars if annual household income is over $25,500 is 63%. Of the households surveyed, 62% had incomes over $25,500 and 44% had 3 cars. The probability that annual household income is over $25,500 if the residents of a household own 3 cars is:

0.89

Suppose X is a uniform random variable over the interval [20, 90]. Find the probability that a randomly selected observation is between 23 and 85.

0.89

Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of 6.1. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 123.

0.9052

One year, professional sports players salaries averaged $1.55 million with a standard deviation of $0.75 million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1.45 million.

0.9088

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 46 minutes and a standard deviation of 11 minutes. A random sample of 25 cars is selected. What is the probability that the sample mean is between 43 and 52 minutes?

0.9105

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective?

0.92

According to a survey result, 79.6% of respondents favored the gun law, 77.8% favored the death penalty for those convicted of murder and 62.7% were in favor of both. What is the probability that a randomly selected respondent was in favor of either the gun law or the death penalty for persons convicted of murder? Hint. Use the addition rules.

0.947

According to the Center for Disease Control, in 2004, 67.5% of all adults between the ages of 18 and 44 were considered current drinkers. Based on this estimate, if three randomly selected adults between the ages of 18 and 44 are selected, what is the probability that at least one is a current drinker?

0.97

Suppose that the probability that a particular brand of light bulb fails before 1000 hours of use is 0.3. If you purchase 3 of these bulbs, what is the probability that at least one of them lasts 1000 hours or more?

0.973

Find the probability that in 40 tosses of a fair six-sided die, a five will be obtained at most 11 times.

0.9739

The height y and base diameter x of five trees of a certain variety produced the following data. Compute the correlation coefficient r. [file:2287.jpg]

0.98

According to the 2003 National Survey on Drug Use and Health, 55.3% of males have never used marijuana. Based on this percentage, what is the probability that more than 50 males who have used marijuana for samples of size 120?

0.9990

The waiting times (in minutes) of customers at the TienPhong Bank, where customers enter a single waiting line that feeds three teller windows, are normally distributed. A random sample of 6 has mean of 7.07 and standard deviation of 0.53. Construct a 94% upper confidence bound for the population standard deviation. Let and

1.06

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the substation?

1.55

Find z if the normal curve area between 0 and z is 0.4756.

1.9703

A committee of three people is to be formed. The three people will be selected from a list of six possible committee members. A simple random sample of three people is taken, without replacement, from the group of six people. Using the letters A, B, C, D, E, F to represent the six people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 20 possible samples.)

1/2

If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT. What is the probability of getting at most one head?

1/2

Pick a bit string from the set of all bit strings of length 10. Find the probability of getting a bit string that begins and ends with 0.

1/4

If two balanced die are rolled, the possible outcomes can be represented as follows. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Determine the probability that the sum of the dice is 7.

1/6

In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at an auto repair shop take per year. A previous study indicated that the standard deviation was 3.2 days. How large a sample must be selected if the company wants to be 95% confident that the true mean differs from the sample mean by no more than 2 day? Let z0.05 = 1.96.

10

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 4%?

1037

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 4%? [file:2235.jpg]

1037

A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%?

1068

A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%? [file:2232.jpg]

1068

Find the mode(s) for the given sample data 11, 13, 11, 23, 22, 24, 56, 22, 72, 15, 27

11 and 22

A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 95% confident that the true mean is within 4 ounces of the sample mean? The standard deviation of the birth weights is known to be 7 ounces.

12

Find the mean for the binomial distribution which has the stated values of n=20 and p=0.6. Round answer to the nearest tenth.

12.0

On a 50-question multiple choice test , each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the random variable X, the number of correct answers.

12.5

A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 2%? A previous study indicates that the proportion of left-handed golfers is 15%.

1225

Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and filterchande at twelve competing service stations: 32.95 24.95 26.95 28.95 18.95 28.95 30.95 22.95 24.95 26.95 29.95 28.95 Compute the range of data.

14

The following data reflect the number of customers who test drove new cars each day for a sample of 20 days at the Redfield Ford Dealership. (See picture) Given these data, what is the range? [file:3562.jpg]

14

(See picture) [file:2257.jpg]

14.573, 43.194

Find the critical value or values of based on the given information. H1: σ < 0.14 n = 25 = 0.10

15.66

For the sample below, find the number of observations that are within 1.5 standard deviations of the mean, i.e. the number of observations lie the interval (μ - 1.5σ; μ + 1.5σ). 2, 3, 5, 5, 6, 3, 6, 5, 6, 9, 2, 5, 3, 5, 6, 3, 5, 6, 6, 9.

16

Find the critical value or values of based on the given information. H0: σ = 8.0/ H1: σ ≠ 8.0 n = 10 α = 0.1

16.92 and 3.33

Let X be a normal random variable with a mean of 18.2 and a variance of 5. Find the value of c if P(X -1 < c) = 0.5221.

17.32

An airline claims that the no-show rate for passengers is less than 3%. In a sample of 420 randomly selected reservations, 21 were no-shows. At = 0.01, compute the value of the test statistic to test the airline's claim.

2.4

For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean.

2.41%

On a 10-question multiple choice test , each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the random variable X, the number of correct answers.

2.5

You wish to test the claim that μ ≤ 38 at a level of significance of α = 0.01 and are given sample statistics n = 43, s =4.7, . Compute the value of the test statistic. Round your answer to two decimal places.

2.51

(See picture) [file:3698.jpg]

2.552

Find the standard deviation for the given sample data: 2 6 2 2 1 4 4 2 4 2 3 8 4 2 2 7 7 2 3 11

2.6

The Hilbert Drug Store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months. He has assumed that the population standard deviation is known to be $14.50. Given this information, what would be the required sample size if we want the total width of the two-side confidence interval on mean to be $4 at 95 percent confidence?

202

A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proprtion by more than 4%? A previous study indicates that the proportion of left-handed golfers is 10%. [file:2222.jpg]

217

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students' scores on the verbal reasoning portion of the GRE follow a normal distribution with a standard deviation of 108. Suppose a random sample of 21 students took the test, and the standard deviation of their scores is 115. What is the test statistic for the test H1: σ ≠ 108.

22.68

The amount of bleach a machine pours into bottles has a mean of 24 oz. with a standard deviation of 1.5 oz. Suppose we take a random sample of 44 bottles filled by this machine. So, 85% of the sample means will be greater than what value?

23.77

Find the standard deviation for the binomial distribution which has the stated values of n = 2661 and p = 0.63. Round your answer to the nearest hundredth.

24.91

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 97% confident that the sample proportion will not differ from the true proportion by more than 7%?

241

The standard IQ test has a mean of 106 and a standard deviation of 12. We want to be 90% certain that we are within 4 IQ points of the true mean. Determine the required sample size.

25

In a manufacturing process that laminates several ceramic layers, 2% of the assemblies are defective. Assume that the assemblies are independent. What is the mean number of assemblies that need to be checked to obtain five defective assemblies?

250

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.55 oz. Suppose we take a random sample of 56 bottles filled by this machine. So, 75% of the sample means will be less than what value?

36.05

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%?

385

Brandon and Samantha each carry a bag containing a banana, a chocolate bar, and a licorice stick. Simultaneously, they take out a single food item and consume it. The possible pairs of food items that Brandon and Samantha consumed are as follows. chocolate bar - chocolate bar licorice stick - chocolate bar banana - banana chocolate bar - licorice stick licorice stick - licorice stick chocolate bar - banana banana - licorice stick licorice stick - banana banana - chocolate bar Find the probability that exactly one chocolate bar was eaten.

4/9

Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: Company A: $73.7 Company F: $26.7 Company B: $63.9 Company G: $26.4 Company C: $57.9 Company H: $22.8 Company D: $57.1 Company I: $21.1 Company E: $32 Company J: $19.8 Calculate the sample variance.

422.940

(See picture) [file:1989.jpg]

5.76

The quality control manager for a filling operation in a bottling plant is concerned with the variability in the volume of milk dispensed into gallon jugs. The filling process results in jugs whose volumes are normally distributed with a mean of 1.02 gallons. The process standard deviation should be less than 0.032 gallons. A sample of 42 jugs was selected and the sample standard deviation was determined to be 0.036 gallons. What is the value of test statistic for the test H1: < 0.032

51.89

The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed.

55.8

The probability that a person has immunity to a particular disease is 0.06. Find the mean for the random variable X, the number who have immunity in samples of size 106.

6.36

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 65,000 miles and a standard deviation of 1500 miles. What warranty should the company use if they want 95% of the tires to outlast the warranty?

62,533 miles

Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid between $148,885 and $151,220 if the standard deviation is $1250.

64.9%

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 362 hours and a standard deviation of 7 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation of the mean?

68%

The number of calls to an Internet service provider during the hour between 6:00 and 7:00 p.m. is described by a Poisson distribution with mean equal to 15. Given this information, what is the expected number of calls in the first 30 minutes?

7.5

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12.4 ounces and a standard deviation of 4.3 ounces. Find the number of ounces above which 86% of the dispensed sodas will fall.

7.8

A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: Find the median of the observations.

74

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.34 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.332 inches?

78.81%

Elaine gets quiz grades of 67, 64, and 87. She gets a 84 on her final exam. Find the mean grade if the quizzes each count for 15% and final exam counts for 55% of the final grade.

78.9

At one college, GPAs are normally distributed with a mean of 2.4 and a standard deviation of 0.3. What percentage of students at the college have a GPA between 2.1 and 2.9?

79.4%

A normal population has mean 76 and variance 9. How large must be the random sample be if we want the standard error of the sample mean to be 1.1?

8

The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings. 11 15 23 29 19 22 21 20 15 25 17 What is the value of IQR?

8

Product codes of 3, 4 or 5 letters are equally likely. What is the mean of the number of letters in 20 codes?

80

A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 4%?

849

A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 94% confident that the error is within 1%?

8836

Assume that the weights of quarters are normally distributed with a mean of 5.73 g and a standard deviation 0.071 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected?

89.73%

The following table is the probability distribution of the number of golf balls ordered by customers x

9.39

It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased. The error sum of squares (SSE) of the above regression is

92.0218

It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students. NOTE: Some of the numbers in the output are purposely erased. The error sum of squares (SSE) of the above regression is [file:3710.jpg]

92.0218

According to a CNN poll taken in February of 2008, 67% of respondents disapproved of the overall job that President Bush was doing. Based on this poll, for samples of size 140, what is the mean number of American adults who disapprove of the overall job that President Bush is doing?

93.8

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 115 mmHg and a standard deviation of 10 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 140 mmHg?

96.5%

(See picture) [file:2185.jpg]

97

Find the mode(s) for the given dample data 98, 25, 98, 13, 25, 29, 56, 98

98

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 110 mmHg and a standard deviation of 10 mmHg. What percentage of 18-year-old women have a systolic blood pressure that lies within 3 standard deviations of the mean?

99.7%

A regional hardware chain is interested in estimating the proportion of their customers who own their own homes. There is some evidence to suggest that the proportion might be around 0.825. Given this, what sample size is required if they wish a 94 percent confidence level with a error of ± 0.025?

About 817

Let X be a continuous random with f(x) is probability density function. Which the following statement(s) is (are) TRUE?

All of them

Which of the following is not an element of descriptive statistical problems?

An inference made about the population based on the sample.

Suppose that an internal report submitted to the managers at a bank in Boston showed that with 95% confidence, the proportion of the bank's customers who also have accounts at one or more other banks is between 0.40 and 0.46. Given this information, what sample size was used to arrive at this estimate?

Approximately 1,066

Suppose that P(A

B) = 0.6, P(A) = 0.5 and P(B) = 0.1. Find the value of P(B|A). | a. 0.12

An entomologist writes an article in a scientific journal which claims that fewer than21 infive thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

H0: p = 0.0042 H1: p < 0.0042

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 20 in every one thousand. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

H0: p = 0.02 H1: p <0.02

It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 28 CEOs and the 99% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the Service industry is less than $3,000,000?

I cannot conclude that the average is less than $3,000,000 at the 99% confidence level.

Suppose a 95% confidence interval for µ turns out to be (1000, 2100). Give a definition of what it means to be 95% confident in an inference.

In repeated sampling, 95% of the intervals constructed would contain the population mean.

Suppose a 95% confidence interval for μ turns out to be (1000, 1900). Give a definition of what it means to be "95% confident" in an inference.

In repeated sampling, 95% of the intervals constructed would contain the population mean.

Suppose a 95% confidence interval for μ turns out to be (1000, 2100). Give a definition of what it means to be 95% confident in an inference.

In repeated sampling, 95% of the intervals constructed would contain the population mean.

Suppose that the random variable X has an exponential distribution with λ = 1.5. Find the mean and standard deviation of X.

Mean = 0.67; Standard deviation = 0.44

Which of the following assignments of probabilities to the sample points A, B, C and D is valid if A, B, C, and D are the only sample points in the experiment?

P(A) = 0, P(B) = , P(C) = , P(D) = 0

The conditional probability of event G, given the knowledge that event H has occurred, would be written as _____.

P(G | H)

The amount of gasoline purchased per car at a large service station is normally distributed with the mean of $47 and a standard deviation of $5. A random sample of 47 is selected, describe the sampling distribution for the sample mean.

Normal with a mean of $47 and a standard deviation of $0.73

Sales prices of baseball cards from the 1980s are known to possess a normal distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 64 cards from the 1980s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards.

Normal with a mean of $5.25 and a standard deviation of $0.35

The heights of people in a certain population are normally distributed with a mean of 64 inches and a standard deviation of 3.1 inches. Determine the sampling distribution of the mean for samples of size 39.

Normal, mean = 64 inches, standard deviation = 0.5 inches

The peak shopping time at home improvement store is between 8-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 150 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that a sapmle of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store.

Number of items - discrete; total time - continuous

Suppose you want to test the claim that μ > 28.6. Given a sample size of n = 62 and a level of significance of . When should you reject H0?

Reject H0 if the test statistic is greater than 2.05

Suppose you want to test the claim that μ ≠ 3.5. Given a sample size of n = 51 and a level of significance of. When should you reject H0 ?

Reject H0 if the test statistic is greater than 2.33 or less than -2.33

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 45°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assume that a hypothesis test of the given claim will be conducted. Identify the type II error for the test.

The error of failing to reject the claim that the mean temperature equals 45°F when it is really different from 45°F.

Carter Motor Company claims that its new sedan, the Libra, will average better than 27 miles per gallon in the city. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

The error of rejecting the claim that the mean is at most 27 miles per gallon when it really is at most 27 miles per gallon.

The principal of a middle school claims that test scores of the seventh-graders at his school varydifferent fromthe test scores of seventh-graders at a neighboring school, which have variation described by σ = 24.1. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

The error of rejecting the claim that the standard deviation is 24.1 when it really is 24.1.

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. Claim: μ = 959. Sample data: n = 25, s = 25. The sample data appear to come from a normally distributed population with σ unknown.

Student t

(See picture) [file:2253.jpg]

Test statistic z = -8.43. There is sufficient evidence to warrant rejection of the claim that the population mean temperature is 22 degree C.

Which of the following is a continuous quantitative variable?

The amount of milk produced by a cow in one 24-hour period

Which of the following is not true about the standard normal distribution?

The area under the standard normal curve to the left of z = 0 is negative.

During one recent year, U.S. consumers redeemed 6.79 billion manufacturers' coupons and saved themselves $2.52 billion. Calculate and interpret the mean savings per coupon.

The average savings was $0.37 per coupon.

A psychologist claims that more than13 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

The error of rejecting the claim that the true proportion is at most 13 percent when it is actually at most 13 percent.

Which of the following is true about the sampling distribution of the sample mean?

The mean of the sampling distribution is always μ.

Which of the following is a discrete random variable?

The number of eggs that hens lay in a month

Which of the following is a discrete quantitative variable?

The number of employees of an insurance company

The owner of a football team claims that the average attendance at games is over 727, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion isrejecting the null hypothesis, state the conclusion in nontechnical terms.

There is sufficient evidence to support the claim that the mean attendance is greater than than 727.

Given the least squares regression line = -2.88- 1.77x and a coefficient of determination of 0.64, the coefficient of correlation is:

a. -0.8

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

a. 0.4332

In 2006, the percent of the voting-age population that was registered to vote for the 50 states and the District of Columbia had a mean of 65% with a standard deviation of 7.1. Assuming that the distribution is normal, what percentage of states had between 50 and 70 percent of it's voting-age population who were registered to vote?

a. 0.74

The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales and the years of experience of 8 randomly selected salespeople. These data are listed below. Years of Experience 0 2 7 4 9 5 5 8 Sales 7 7.7 15 8.5 15 7 8 12 Determine the correlation coefficient.

a. 0.81

Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and filterchande at twelve competing service stations: Compute the range of data.

a. 14

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within 0.08 using 95% confidence?

a. 150

You want to explore the relationship between the grades students receive on their first two exams. For a sample of 17 students, you find a correlation coefficient of 0.47. What is the value of the test statistic for testing H0: ρ = 0 vs. H1: ρ 0 ?

a. 2.06

On a 10-question multiple choice test , each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the random variable X, the number of correct answers.

a. 2.5

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes. Find the number of minutes, m, for which the probability that a customer spends less than m minutes in the supermarket is 0.10.

a. 37.3

Brandon and Samantha each carry a bag containing a banana, a chocolate bar, and a licorice stick. Simultaneously, they take out a single food item and consume it. The possible pairs of food items that Brandon and Samantha consumed are as follows. chocolate bar - chocolate bar licorice stick - chocolate bar banana - banana chocolate bar - licorice stick licorice stick - licorice stick chocolate bar - banana banana - licorice stick licorice stick - banana banana - chocolate bar Find the probability that at least one chocolate bar was eaten.

a. 5/9

If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT. What is the probability of getting at least one head?

a. 7/8

The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height. Round your answer to one decimal place.

a. 76.4

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Hours,x 3 5 2 8 2 4 4 5 6 3 Scores,y 65 80 60 66 78 85 90 90 71 88 Find the equation of the regression line for the given data.

a. = -0.24x + 78.31

The use of the Poisson distribution requires a value n which indicates a definite number of independent trials.

a. False

To determine the mean of a binomial distribution, it is necessary to know the number of successes involved in the problem.

a. False

You want to explore the relationship between the scores students receive on their first quiz and their first exam. You believe that there is anegative correlation between the two scores. What are the most appropriate null and alternative hypotheses regarding the population correlation?

a. H0: ρ = 0 and H1: ρ < 0

Which of the following is always true?

a. If A and B are disjoint, then they cannot be independent.

Survey responses of temperatures of the ocean at various depths. which type of data is?

a. Interval

In a regression problem the following pairs of (x, y) are given: (-4, 8), (-1, 2), (0, 0), (1, -2) and (4, -8). What does this indicate about the value of coefficient of determination?

a. It is +1.

Based on the scores 1, 9, 3, 6, 1, 2, 6, 2, 2, and 8, a score of 4 is the

a. mean.

In a pizza takeout restaurant, the following probability distribution was obtained. The random variable X represents the number of toppings for a large pizza. Find the mean and standard deviation for the random variable X. x 0 1 2 3 4 P(x) 0.30 0.40 0.20 0.06 0.04

a. mean: 1.14; standard deviation: 1.04

The random variableX represents the number of girls in a family of three children. Assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable X.

a. mean: 1.50; standard deviation: 0.87

An economist is interested in studying the incomes of consumers in a particular region. The normally population standard deviation is known to be $1000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100? Let $$z_{0.025}=1.96; z_{0.05}=1.65$$.

a. n = 1537

Given the supply of a commodity, x, and the price of a commodity, y, would you expect a positive correlation, a negative correlation, or no correlation?

a. negative correlation

To determine the difference , if any, between two brands of radial tires, 12 tires of each brand are tested. Assume that the lifetimes of both brands of tires come from the same normal distribution N(m, 33002). The distribution of the difference of the sample mean $$\overline{X}$$ - $$\overline{Y}.$$

a. normal with mean 0 and standard deviation 1347.22

We can show that, when the null hypothesis H0: ρ = 0 is true and the random variables have a joint normal distribution, then the random variable which is used to test the hypothesis that there is no linear association in the population between a pair of random variables, follows the:

a. student's t distribution.

An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. What is the sample?

a. three selected custermers

A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a population standard deviation of 31 hours. Construct a 95% confidence interval for the population mean.

b. (636.9, 653.1)

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be exactly 3 power outages in a year is

b. 0.0892

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is

b. 0.10

The weekly salaries of elementary school teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected elementary school teacher earns more than $525 a week?

b. 0.2177

After completing an inventory of three warehouses, a golf club shaft manufacturer described its stock of 12,246 shafts with the percentages given in the table. Suppose a shaft is selected at random from the 12,246 currently in stock, and the warehouse number and type of shaft are observed. Type of Shaft Given that the shaft is produced in warehouse 2, find the probability it has an extra stiff shaft.

b. 0.219

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income less than or equal to $25,000 a year is:

b. 0.22

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 40 to 80. What is the probability that this experiment results in an outcome less than 50?

b. 0.25

Use the given information to find the P-value. The test statistic in a right-tailed test is z = 0.52.

b. 0.3015

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

b. 0.60653

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 8.5 to 10.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 9.2 millimeters?

b. 0.65

The distribution of B.A. degrees conferred by a local college is listed below, by major. Major Frequency Engineering 868 English 2073 Mathematics 2164 Chemistry 318 Physics 856 Liberal Arts 1358 Business 1676 What is the probability that a randomly selected degree is not in Mathematics?

b. 0.768

The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media. X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05 $$ The variance for the number of retransmissions is

b. 0.8

A salesperson knows that 20% of his presentations result in sales. Find the probabilities that in the next 60 presentations between 14 and 18, inclusive, result in sales. (Note: please give the answer as a real number accurate to 4 decimal places after the decimal point.)

b. 0.98

Suppose that the probability that a particular brand of light bulb fails before 900 hours of use is 0.2. If you purchase 3 of these bulbs, what is the probability that at least one of them lasts 900 hours or more?

b. 0.992

Six pairs of data yield $$r = 0.444$$ and the regression equation $$\hat y= 5x+2.$$ Also, $$\overline{y}=18.3$$. What is the best predicted value of $$y$$ for $$x=5$$?

b. 18.3

A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%? A previous study indicates that the proportion of left-handed golfers is 10%.

b. 217

Compute the standardized test statistic, $$\chi^2$$, to test the claim $$\sigma^2= 34.4$$ if $$n = 12, s =28.8$$, and $$\alpha=0.05$$.

b. 265.23

The produce manager at a food store was interested in determining how many apples a person buys when they buy apples. He asked the cashiers over a weekend to count how many apples a person bought when they bought apples and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of apples purchased and P(x) represents the probability that a customer will buy x apples. Determine the variance of the number of apples purchased by a customer. x 1 2 3 4 5 6 7 8 9 10 P(x) 0.05 0.19 0.20 0.25 0.12 0.10 0 0.08 0 0.01

b. 3.57

A random sample of 20 observations was made on the diameter of spot welds and the corresponding weld shear strength. Given that r = 0.65, what is the value of test statistic if we want to test the hypothesis that ρ = 0 at a level of significance of 0.05. Let t0.025,18 = 2.1, t0.05,18 = 1.73 and t0.025,19 = 2.09.

b. 3.63

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the Manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month. Miles traveled, x 4 8 10 Sales, y 27 58 61 Calculate the test statistic to test the claim ρ = 0. Round answers to three decimal places.

b. 3.857

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. So, 90% of the sample means will be greater than what value?

b. 41.8 minutes

The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 3 randomly selected adults. Age, x 42 45 49 Pressure, y 118 122 125 Calculate the test statistic to test the claim ρ = 0. Round answers to three decimal places.

b. 5.913

Suppose X is a uniform random variable over the interval [40, 70]. Find the standard deviation of X.

b. 8.66

The number of golf balls ordered by customers of a pro shop has the following probability distribution. x 3 6 9 12 15 P(x) 0.14 0.11 0.36 0.29 0.10 Find the mean of thethis probability distribution.

b. 9.3

For the data in the table below, find the equation of the regression line of y on x. x 0 1 2 1 y 0 0 1 3

b. = 0.5x +0.5

A mail-order firm is interested in estimating the number of order that need to be processed on a given day from the weight of the mail received. A close monitoring of the mail on 4 randomly selected business days produced the results below. Find the equation of the least squares regression line relating the number of orders to the weight of the mail. Mail: x (pounds) 10 12 13 17 Orders: y 8 10 6 10

b. = 5.5 + 0.23x

Which of the following statements is true regarding the coefficient of correlation?

b. All of the others

Suppose a 95% confidence interval for population mean turns out to be (1000, 2100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?

b. Both increase the sample size and decrease the confidence level.

An entomologist writes an article in a scientific journal which claims that fewer than 11 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

b. H0: p = 0.0011 H1: p < 0.0011

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three boys in ten births.

c. 0.172

The principal of a middle school claims that test scores of the seventh-graders at her school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by σ = 14.7. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

b. H0: σ = 14.7 H1: σ < 14.7

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the σ = 3.3 mg claimed by the manufacturer. Express the null hypothesis H 0 and the alternative hypothesis H 1 in symbolic form.

b. H0:σ = 3.3 mg H1:σ ≠ 3.3 mg

The table below shows the legal costs and the profits of a company from 2000 to 2005. Construct a scatter diagram for the data and state whether legal costs and profits for this company have no correlation, a positive correlation, or a negative correlation for this period.

b. Negative correlation

Which of the following is always true for a normal distribution?

b. P(2< x ≤ 8) = P(2 ≤ x < 8)

The following table gives the total sales (revenue) and profits for 8 retailers. Construct a scatter diagram for the data and state whether sales and profits for these companies have no correlation, a positive correlation, or a negative correlation.

b. Positive correlation

For a random sample of 263 professionals, the correlation between their age and their income was found to be 0.17. You are interested in testing the null hypothesis that there is no linear relationship between these two variables against the alternative that there is a positive relationship. What is your conclusion in testing H0: ρ = 0 vs. H1: ρ > 0 at = 0.01?

b. Reject H0

49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classed with 496, 348, and 481 students respectively. Identify which of these types of sampling is used: Stratified, systematic, cluster, random.

b. Stratified

The number of monthly breakdowns of a conveyor belt at a local factory is a random variable having the Poisson distribution with λ = 2.8. Find the probability that the conveyor belt will function for a month with one breakdown. (Note: please give the answer as a real number accurate to2 decimal places after the decimal point.)

b. There is not sufficient evidence to support the claim that the true proportion is less than 3 in ten thousand.

A researcher claims that 62% of voters favor gun control. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

b. There is not sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control.

For two events A and B, P(A) = 0.8, P(B) = 0.2, and P(A and B) = 0.16. It follows that A and B are

b. independent but not disjoint.

Given the supply of a commodity, x, and the price of a commodity, y, would you expect a positive correlation, a negative correlation, or no correlation?

b. negative correlation

Assume that you are predicting Y from X. Which of the following correlation coefficients would yield predictions with the least error?

b. r = -0.85

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $25,000 a year is:

c. 0.12

Find the normal-curve area between z = -2 and z = -1.

c. 0.1359

A study of the amount of time it take a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.

c. 0.1469

The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.27 ounces and a standard deviation of 0.18 ounce. The cans only hold 12.45 ounces of soda. Every can that has more than 12.45 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process?

c. 0.1587

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces. Find the probability that more than 16 ounces is dispensed in a cup.

c. 0.1587

An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, he collected the age at death (y), the average number of hours of exercise per week (x). A random sample of 7 individuals was selected and the results are shown below. x 7 8 6 7 12 12 3 y 85 80 75 79 82 79 80 Determine the correlation coefficient.

c. 0.17

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, X. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the following table. X(girls) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 P(X) 0.000 0.001 0.006 0.022 0.061 0.122 0.183 0.209 0.183 0.122 0.061 0.022 0.006 0.001 0.000 Find the probability of selecting 9 or more girls.

c. 0.212

If a random variable has the normal distribution with μ = 30 and σ = 5, find the probability that it will take on the value between 24 and 28.

c. 0.2295

An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 549 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 99% confidence level.

c. 0.37 ± .053

A group of volunteers for a clinical trial consists of 83 women and 78 men. 21 of the women and 20 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person is a man given that they have high blood pressure.

c. 0.488

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean is between 45 and 52 minutes?

c. 0.4947

Assume that X has a normal distribution with the mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 15.2.

c. 0.5000

Suppose that a number of miles that a car can run before its battery wears out is exponentially distributed with an average value of 10000 miles. If a person desires to take a 5000-mile trip, what is the probability that she will be able to complete her trip without having to replace her car battery?

c. 0.6

Let X be a uniform random variable over the interval [0, 8] . What is the probability that the random variable X has a value greater than 3?

c. 0.625

Consider a random sample of 27 observations of two variables X and Y. The following summary statistics are available: Σyi = 57.2,Σxi = 1253.4, = 73296.4, and Σxiyi = 3133.7. What is the y-intercept of the sample regression line?

c. 0.649

Assume that X has a normal distribution with the mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is between 14.3 and 16.1.

c. 0.6826

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes. Find the probability that a customer spends less than 48 minutes in the supermarket.

c. 0.6915

The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.0 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 2.5 and 5.0 minutes to find a parking spot in the library lot.

c. 0.7745

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at most 40 times.

c. 0.9105

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 2.8 minutes. What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?

c. 0.917915

In 2006, the General Social Survey asked subjects whether they favored or opposed the death penalty for persons convicted of murder and whether they favored or opposed a law requiring a person to obtain a permit before he or she could buy a gun. According to the survey results, 79.6% of respondents favored the gun law, 67.8% favored the death penalty for those convicted of murder and 52.7% were in favor of both. What is the probability that a randomly selected respondent was in favor of either the gun law or the death penalty for persons convicted of murder? Hint. Use the addition rules.

c. 0.947

A percentage distribution is given below for the size of families in one U.S. city. Size Percentage 2 45.1 3 22.2 4 19.7 5 8.0 6 3.1 7+ 1.9 A family is selected at random. Find the probability that the size of the family is less than 6. Round your result to three decimal places.

c. 0.950

Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected?

c. 1.96%

Suppose we have the following information from a simple regression: n = 15, = 301.5, = 385.7, = 1719.8, = 1200.9, = 1090.5. What is the y-intercept of the regression line of hours on income?

c. 12.97

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

c. 2.28%

A recent study of 60 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.01, the critical value for the test to determine whether the true population correlation coefficient is zero is:

c. 2.66

Find the percentile for the data point. Data set: 51 36 48 75 75 75 49 data point: 51

c. 43

According to the 2003 National Survey on Drug Use and Health, 54.3% of males have never used marijuana. Based on this percentage, what is the expected number of males who have used marijuana for samples of size 100?

c. 45.7

If a psychologist observed that four 5-year-old children initiated 2, 4, 6, and 12 incidents of aggression during a play period, the mean number of aggressive incidents for this group of four children was

c. 6

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. Find the waiting time at which only 10% of the customers will continue to hold.

c. 6.9 minutes

A sample of 8 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 1820.875, = 1150, = 1080.5. What is the regression sum of squares?

c. 641.164

At one college, GPAs are normally distributed with a mean of 2.6 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.2 and 3?

c. 68%

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 360 hours and a standard deviation of 5 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation of the mean?

c. 68%

Suppose you are interested in determining the relationship between the number of absences (x) and the final grades (y) of students from a statistics class. For a sample of 9 observations, you have the following information: Σxi = 217, Σyi = 131.7, Σxiyi = 1932.5, Σ(xi)2 = 689, Σ(yi)2 = 1321.5. Find the sample regression line.

c. = 8.027 + 0.274x

A psychologist claims that more than 6.3 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

c. H0: p = 6.3% H1: p > 6.3%

The owner of a football team claims that the average attendance at games is over 67,800, and he is therefore justified in moving the team to a city with a larger stadium. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form.

c. H0: μ, the average attendance at games, is equal to 67,800 H1: μ, the average attendance at games, is greater than 67,800

A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?

c. Maybe. 0.60 is a believable value of the population proportion based on the information above.

Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%. Create the sample space of possible outcomes.

c. NNR NNN

The table below shows the legal costs and the profits of a company from 2000 to 2005. Construct a scatter diagram for the data and state whether legal costs and profits for this company have no correlation, a positive correlation, or a negative correlation for this period.

c. Negative correlation

For a group of English students at the local junior college, the scatter diagram compares the number of incorrect answers on a test they took (y) and the length of the pencil used to take the test (x). State whether there is no correlation, a positive correlation, or a negative correlation between the x and y variables.

c. No correlation

The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag. Identify which of these types of sampling is used: Stratified, systematic, cluster, random.

c. Random

For a random sample of 263 professionals, the correlation between their age and their income was found to be 0.17. You are interested in testing the null hypothesis that there is no linear relationship between these two variables against the alternative that there is a positive relationship. What is your conclusion in testing H0: ρ = 0 vs. H1: ρ > 0 at = 0.01?

c. Reject H0

The owner of a football team claims that the average attendance at games is over 727, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

c. There is not sufficient evidence to support the claim that the mean attendance is greater than 727.

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the σ = 3.3 mg claimed by the manufacturer. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

c. There is not sufficient evidence to support the claim that the standard deviation is different from 3.3 mg

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1000. A random sample of 50 individuals resulted in an average income of $15000. What is the width of the 90% confidence interval?

d. $465.23

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677.

d. ($2803, $3437)

Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they watched television was 19.6 with a standard deviation of 5.8 hours.

d. (17.47, 21.73)

Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78.

d. (2.51, 3.21)

For a sample of 45 observations, you have the following information: Σxi = 153.7, Σyi = 231.2, Σxiyi = 712.5, Σ(xi)2 = 718, Σ(yi)2 = 1775.2. What is the sample correlation coefficient between X and Y?

d. -0.23

Given the least squares regression line = -2.88- 1.77x and a coefficient of determination of 0.64, the coefficient of correlation is:

d. -0.8

For a sample of 10 observations, you have the following information: Σxi = 253, Σyi = 172.2, Σxiyi = 643.4, Σ(xi)2 = 696, Σ(yi)2 = 152.2. What is the sample correlation coefficient between X and Y?

d. -0.93

Which of the following represents the strongest linear correlation?

d. -0.97

Consider a random sample of 20 observations of two variables X and Y. The following summary statistics are available: Σyi = 12.75,Σxi = 1478, = 143,215.8, and Σxiyi = 1083.67. What is the slope of the sample regression line?

d. 0.0042

It has been found that 40% of the employees who complete a sequence of executive seminars go on to become vice presidents. Assume that 10 graduates of the program are randomly selected. Find the probability that at least three become vice presidents. (Note: please give the answer as a real number accurate to3 decimal places after the decimal point.)

d. 0.0064

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

d. 0.0166

The average score of all golfers for a particular course has a mean of 79 and a standard deviation of 5. Suppose 100 golfers played the course today. Find the probability that the average score of the 100 golfers exceeded 80.

d. 0.0228

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger?

d. 0.0228

The time for a worker to assemble a component is normally distributed with mean 15 minutes and variance 4. Denote the mean assembly times of 16 day-shift workers and 9 night-shift workers by $$\overline{X}$$ and $$\overline{Y}$$, respectively. Assume that the assembly times of the workers are mutually independent.ComputeP($$\overline{X} $$ - $$\overline{Y}$$ < -1.5) is

d. 0.0359

For women aged 18-24, systolic blood pressures ( in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 23 women aged 18-24 are randomly selected, find the probability that their mean systolic blood pressures is between 119 and 122.

d. 0.0577

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil will be less than 0.285 inches?

d. 0.0668

The data below are the exam scores of 4 randomly selected statistics students, what is the value of the test statistic for testing Mid-term, x 5 6 6 7.4 Final, y 5.2 4.6 7 7

d. 0.07

Find the normal-curve area between z = -1.48 and z = 0.

d. 0.4306

The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 4.5 to 6.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 5.2 millimeters?

d. 0.65

It has been found that 40% of the employees who complete a sequence of executive seminars go on to become vice presidents. Assume that 10 graduates of the program are randomly selected.Find the probability that exactly 5 become vice presidents. (Note: please give the answer as a real number accurate to3 decimal places after the decimal point.)

d. 0.67

For two events A and B, P(A) = 0.4, P(B) = 0.5. Then P(A or B) equals

d. 0.7, if A and B are independent.

The age distribution of students at a community college is given below. Age (years) Number of students Under 21 409 21-24 404 25-28 276 29-32 155 33-36 97 37-40 63 Over 40 86 A student from the community college is selected at random. Find the probability that the student is 21 years or over. Give your answer as a decimal rounded to three decimal places.

d. 0.726

The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales and the years of experience of 8 randomly selected salespeople. These data are listed below. Years of Experience 0 2 7 4 9 5 5 8 Sales 7 7.7 15 8.5 15 7 8 12 Determine the correlation coefficient.

d. 0.81

A salesperson knows that 20% of her presentations result in sales. Find the probabilities that in the next 60 presentations at least 9 result in sales.

d. 0.8732

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?

d. 0.8767

According to the Center for Disease Control, in 2004, 65.7% of all adults between the ages of 18 and 44 were considered current drinkers. Based on this estimate, if two randomly selected adults between the ages of 18 and 44 are selected, what is the probability that at least one is a current drinker?

d. 0.88

Consider the following pairs of observations: x 2 3 5 5 7 6 y 1.3 1.5 2.2 2.3 2.7 1.9 Find the value of the coefficient of correlation.

d. 0.897

A survey of senior citizens at a doctor's office shows that 52% take blood pressure-lowering medication, 43% take cholesterol-lowering medication, and 5% take both medications. What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication?

d. 0.90

The age distribution of students at a community college is given below. Age (years) Number of students Under 21 416 21-24 419 25-28 263 29-32 151 33-36 93 37-40 59 Over 40 85 A student from the community college is selected at random. Find the probability that the student is under 37 years old. Give your answer as a decimal rounded to three decimal places.

d. 0.903

Recently, an automobile insurance company performed a study of a random sample of 38 of its customers to determine if there is a positive relationship between the number of miles driven and the age of the driver. The sample correlation coefficient is r = 0.59. Given this information, which of the following is appropriate critical value for testing the null hypothesis at an alpha = 0.05 level?

d. 1.688

A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 3%? A previous study indicates that the proportion of households with two cars is 24%.

d. 1101

Suppose we have the following information from a simple regression: n = 15, = 301.5, = 385.7, = 1719.8, = 1200.9, = 1090.5. What is the y-intercept of the regression line of hours on income?

d. 12.97

According to a CNN poll taken in February of 2008, 67% of respondents disapproved of the overall job that President Bush was doing. Based on this poll, for samples of size 200, what is the mean number of American adults who disapprove of the overall job that President Bush is doing?

d. 134

The probability that a person has immunity to a particular disease is 0.6. Find the mean for the random variable X, the number who have immunity in samples of size 26.

d. 15.6

A recent study of 60 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.01, the critical value for the test to determine whether the true population correlation coefficient is zero is:

d. 2.66

A sample of 8 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 1820.875, = 1150, = 1080.5. What is the regression sum of squares?

d. 641.164

The height y and base diameter x of five tree of a certain variety produced the following data x 1 2 2 5 y 30 40 90 120 Find the equation of the estimated regression line of y on x.

d. = 21.11x+17.22

You want to explore the relationship between the scores students receive on their first quiz and their first exam. You believe that there is anegative correlation between the two scores. What are the most appropriate null and alternative hypotheses regarding the population correlation?

d. H0: ρ = 0 and H1: ρ < 0

It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the Service industry is more than $3,000,000?

d. I cannot conclude that the average exceeds $3,000,000 at the 97% confidence level.

In a regression problem the following pairs of (x, y) are given: (-4, 8), (-1, 2), (0, 0), (1, -2) and (4, -8). What does this indicate about the value of coefficient of determination?

d. It is +1.

Suppose that the random variable X has an exponential distribution with λ = 1.5. Find the mean and standard deviation of X.

d. Mean = 0.67; Standard deviation = 0.44

The following table gives the total sales (revenue) and profits for 8 retailers. Construct a scatter diagram for the data and state whether sales and profits for these companies have no correlation, a positive correlation, or a negative correlation.

d. Positive correlation

The table below shows the sales and profits of a company from 2000 to 2005. Construct a scatter diagram for the data and state whether sales and profits for this company have no correlation, a positive correlation, or a negative correlation for this period.

d. Positive correlation

For a random sample of 263 professionals, the correlation between their age and their income was found to be 0.17. You are interested in testing the null hypothesis that there is no linear relationship between these two variables against the alternative that there is a positive relationship. What is your conclusion in testing H0: ρ = 0 vs. H1: ρ > 0 at = 0.01?

d. Reject H0

A sample consists of every 49th student from a group of 496 students. Identify which of these types of sampling is used: Stratified, systematic, cluster, random.

d. Systematic

The process of using sample statistics to draw conclusions about true population parameters is called

d. statistical inference.

We can show that, when the null hypothesis H0: ρ = 0 is true and the random variables have a joint normal distribution, then the random variable which is used to test the hypothesis that there is no linear association in the population between a pair of random variables, follows the:

d. student's t distribution.

Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 210 students and carefully recorded their parking times. Identify the population of interest to the university administration.

d. the parking times of the entire set of students that park at the university

The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment?

d. {0, 1, 2}

The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of

descriptive statistics.

Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called

descriptive statistics.

(See picture) [file:1867.jpg]

disjoint but not independent.

For two events A and B, P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0. It follows that A and B are

disjoint but not independent.

A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.)

e.

Suppose we have the following information from a simple regression: = 107.4, = -14.39, se()= 2.8, se()= 2.4, n = 200. What is the value of the test statistic for testing H0: ?

e. -1.071

The data below are the exam scores of 4 randomly selected statistics students, what is the value of the test statistic for testing Mid-term, x 5 6 6 7.4 Final, y 5.2 4.6 7 7

e. 0.07

Assume that we found out the regression equation = 1.6 +x corresponding to the data below x 0 1 2 4 5 y 1 2 4 5 7 Find the error sum of square SSE.

e. 0.919

A company keeps extensive records on its new salespeople on the premise that sales should increase with experience. A random sample of seven new salespeople produced the data on experience and sales shown in the table. Months on job, x 2 12 5 9 7 Monthly sales, y 2.4 15.0 3.5 11.0 10.5 Find the value of the coefficient of correlation.

e. 0.96

The weight and systolic blood pressure of 4 randomly selected males in the age group 25 to 30 are shown in the following table. Assume that weight and blood pressure are jointly normally distributed. Weight, x 50 62 67 55 Pressure, y 90 110 100 90 What is the value of the test statistic for testing

e. 1.46

Recently, an automobile insurance company performed a study of a random sample of 38 of its customers to determine if there is a positive relationship between the number of miles driven and the age of the driver. The sample correlation coefficient is r = 0.59. Given this information, which of the following is appropriate critical value for testing the null hypothesis at an alpha = 0.05 level?

e. 1.688

A recent study of 60 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.01, the critical value for the test to determine whether the true population correlation coefficient is zero is:

e. 2.66

A sample of 8 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 1720.875, = 1150, = 1090.5. What is the y-intercept of the regression line of hours on income?

e. 23.46

A random sample of 20 observations was made on the diameter of spot welds and the corresponding weld shear strength. Given that r = 0.65, what is the value of test statistic if we want to test the hypothesis that ρ = 0 at a level of significance of 0.05. Let t0.025,18 = 2.1, t0.05,18 = 1.73 and t0.025,19 = 2.09.

e. 3.63

A sample of 8 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 1720.875, = 1050, = 1080.5. What is the error sum of squares?

e. 371.578

For the data in the table below, find the equation of the regression line of y on x. x 0 1 2 1 y 0 0 1 3

e. = 0.5x +0.5

The height y and base diameter x of five tree of a certain variety produced the following data x 1 2 2 5 y 30 40 90 120 Find the equation of the estimated regression line of y on x.

e. = 21.11x+17.22

A sample of10 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 15210, = 17150, = 2599. What is the value of the coefficient of determination?

e. None of the other choices is true

Carter Motor Company claims that its new sedan, the Libra, will average better than 23 miles per gallon in the city. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.

gallon when it really is at most 23 miles per gallon.

For two events A and B, P(A) = 0.8, P(B) = 0.2, and P(A and B) = 0.16. It follows that A and B are

independent but not disjoint.

Given events C and D with probabilities P(C) = 0.3, P(D) = 0.2, and P(C and D) = 0.1, are C and D independent?

no

Sampling distributions describe the distribution of

statistics.

Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 210 students and carefully recorded their parking times. Identify the population of interest to the university administration.

the parking times of the entire set of students that park at the university

A bag of colored candies contains 20 red, 25 yellow, 15 blue and 20 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment?

{red, yellow, blue, orange}

Suppose X has a Poisson probability distribution with = 9.0. Find μ and σ.

μ = 9.0, σ = 3.0

The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with $$\mu= 110$$ grams and $$\sigma = 25$$ grams. A sample of vitamins is to be selected. What is the probability that the sample mean will be less than 100 grams? Let $$P(Z<-2)=0.023;P(Z<-0.4)=0.421;P(Z<0.07)=0.529;P(Z<0.75)=0.673$$.

a. 0.023

LetZ is a standard normal variable, find the the probability that Z lies between 0 and 3.01.

a. 0.4987

A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed. $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00 Find the 95% confidence interval for the true mean.

b. ($3.39, $6.01)

If the probability of a newborn child being female is 0.5, find the probability that in 100 births, 55 or more will be female.

b. 0.1841

Find the critical value or values of x2 based on the given information. H1: σ < 0.629 n = 19 α = 0.025

b. 8.231

The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

d. 0.4013

A psychologist claims that more than 75 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

b. There is not sufficient evidence to support the claim that the true proportion is greater than 75 percent.

A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment?

b. {red, yellow, orange}

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours.

c. (628.5, 661.5)

A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls followed a normal distribution with an average of $900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, what is the probability that a randomly selected month had a PCE of between $775.00 and $990.00?

c. .9579

The probability is 2% that an electrical connector that is kept dry fails during the warranty period of a portable computer. If the connector is ever wet, the probability of a failure during the warranty period is 10%. If 80% of the connectors are kept dry and 20% are wet, what proportion of connectors fail during the warranty period?

c. 0.036

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at least 40 times.

c. 0.1210

Find the mean for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 20; p = 3/5

c. 12.0

A card game is played in which the player wins if a face card is drawn (king, queen, jack) from a deck of 52 cards. If the player plays 10 times, what is the expected number of wins for the player?

c. 2.31

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. Find the variance for the probability distribution. x 1 2 3 4 5 6 P(x) 0.16 0.19 0.22 0.21 0.12 0.10

c. 2.36

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following confidence interval: Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within 2% using 99% reliability?

c. 4118

The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

c. There is sufficient evidence to support the claim that the standard deviation is less than 14.7.

When considering area under the standard normal curve, decide whether the area to the left ofz =0.2is bigger than, smaller than, or equal to the area to the right ofz = -0.2

c. equal to

A local bank needs information concerning the checking account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 98% confidence interval for the true mean. Assume that the account balances are normally distributed.

d. ($513.17, $860.33)

Construct a 99% confidence interval for the population mean, μ. Assume the population has a normal distribution. A group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

d. (19.9, 24.9)

A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $700 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the probability that a randomly selected month had a PCE that falls below $550.

d. 0.0013

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n =12, x = 5, p = 0.25

d. 0.103

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective?

d. 0.1175

A machine is set to pump cleanser into a process at the rate of 5 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 4.5 to 7.5 gallons per minute. Find the probability that between 5.0 gallons and 6.0 gallons are pumped during a randomly selected minute.

d. 0.33

A percentage distribution is given below for the size of families in one U.S. city. Size Percentage 2 42.8 3 21.1 4 19.2 5 11.6 6 3.3 7+ 2.0 A family is selected at random. Find the probability that the size of the family is 4 or more. Round your result to three decimal places.

d. 0.361

Let X represent the amount of time it takes a student to park in the library parking lot at the university. If we know that the distribution of parking times can be modeled using an exponential distribution with a mean of 4 minutes, find the probability that it will take a randomly selected student between 2 and 12 minutes to park in the library lot.

d. 0.556744

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the substation?

d. 1.55

When conducting a t test for the correlation coefficient in a study with 16 individuals, the degrees of freedom will be

d. 14.

For the sample below, find the number of observations that are within 1.5 standard deviations of the mean. 2, 3, 5, 5, 6, 3, 6, 5, 6, 9, 2, 5, 3, 5, 6, 3, 5, 6, 6, 9.

d. 16

Find the variance for the given probability distribution. x 0 1 2 3 4 P(x) 0.17 0.28 0.05 0.15 0.35

d. 2.46

The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n= 647 drowning deaths of children with 30% of them attributable to beaches. Find the value of the test statistic z using $$z=\frac{\overline{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$$.

d. 2.94

The standard IQ test has a mean of 96 and a standard deviation of 14. We want to be 90% certain that we are within 4 IQ points of the true mean. Determine the required sample size.

d. 34

Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children's clothing should be manufactured and marketed in larger sizes. If $$X$$ is the weight of school children sampled in a nationwide study, then $$X$$ is an example of

d. a continuous random variable.