MAS291

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

a. Nomial

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

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

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

d. 0.2525

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 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

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

a. 0.7557

Construct the relative frequency distribution that corresponds to given frequency distribution

b.

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)

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

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.

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

c. 0.0336

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

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.

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

c. Ordinal

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

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}

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)

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

d. 98

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

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

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)

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

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

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

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

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.

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

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%

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

d. all custormers

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%.

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

a.

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)

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

a. 0.0436

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

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

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

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 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

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

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

a. 0.4987

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

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

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

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

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

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 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%

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

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.

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 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)

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)

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

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

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

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

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

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

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

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 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.

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.

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.

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

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

c. 0.0764

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

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

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

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

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

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 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

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

c. 31.74%

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

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

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%

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

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.

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

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

d.

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)

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

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

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.

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