Exam 2

A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400 = .375 (to 4 decimals)? Use z-table.

0.8461

Exhibit 5-10 The probability distribution of the number of goals the Lions soccer team makes per game is given below Number of Goals Probability 0 0.05 1 0.15 2 0.35 3 0.30 4 0.15 Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score at least 1 goal?

0.95

A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is...

0.9544

Assume that you have a binomial experiment with p = 0.3 and a sample size of 100. The expected value and variance are ____ and _____, respectively

30, 21

The random variable x is known to be uniformly distributed between 1.0 and 1.5. What is P(x = 1.25)?.

0.00

X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that X equals 19.62 is

0.000

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that X is greater than 10.52 is

0.0029

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is...

0.0200

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is...

0.0228

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

0.0142

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were female. The standard error of the proportion is...

0.0400

Given that z is a standard normal random variable, what is P(z > 1.52)?

0.0643

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is...

0.0668

The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend would spend an average $749 (The Associated Press, August 12, 2012). Assume that the amount spent is normally distributed with a standard deviation of $225. What is the probability that family expenses for the weekend will be between $700 and $800?

0.1781

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 15 students registered for the course. What is the probability that at least 4 students will withdraw from the course (use the binomial distribution table (z-table).

0.1876

The probability density function for a uniform distribution ranging between 2 and 6 is

0.25

Given that z is a standard normal random variable, what is P(0.51 < z < 2.17)?

0.2900

Ten Percent (10%) of the customers of a mortgage company default on their payments. A sample of 5 customers is selected. What is the probability that exactly one customer in the sample will default on his/her payments? (Use the binomial probability formula).

0.328

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,000 and $15,000. Suppose you bid $12,000. What is the probability that your bid will be accepted? (i.e., what is the probability that x (your competitor's bid would be less than $12,000?)

0.40

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,000 and $15,000. Suppose you bid $13,000. What is the probability that your bid will not be accepted? (i.e., what is the probability that x (your competitor's bid would be greater than $13,000?)

0.40

For the standard normal probability distribution, the area to the left of the mean is

0.5

The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend would spend an average $749 (The Associated Press, August 12, 2012). Assume that the amount spent is normally distributed with a standard deviation of $225. What is the probability of family expenses for the weekend being less than $749?

0.5000

A population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within ± 2 of the population mean?

0.6826

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 15 students registered for the course. What is the probability that at least 2 students will withdraw from the course (use the binomial distribution table (z-table).

0.8329

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12 respectively. The standard error of the mean is...

1.20

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1112?

1.22

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are...

200 and 2

A population has a mean of 75 and a standard deviation of 8. A random sample of 800 is selected. The expected value of is...

75

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a...

Discrete Random Variable

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

The Trials Are Dependent

Which of the following is not a characteristic of the normal probability distribution?

The standard deviation must be 1

People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. Use z-table. a. Show the sampling distribution of (P), the proportion of groceries thrown out by your sample respondents (to 4 decimals). b. What is the probability that your survey will provide a sample proportion within ±.03 of the population proportion (to 4 decimals)? c. What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion (to 4 decimals)?

a(a). Can assume the be normally distributed because np> = 5 and n(1 - p) > = 5 a(b). p = 0.12 b. 0.9676 c. 0.7154

Allegiant Airlines charges a mean base fare of $88. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $34 per passenger. Suppose a random sample of 80 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $36. Use z-table. a. What is the population mean cost per flight? b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)? c. What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?

a. $122 b. 0.9868 c. 0.7850

Given that z is a standard normal random variable, find z for each situation (to 2 decimals). Use Table 1 in Appendix B. a. The area to the left of z is 0.2119 b. The area between -z and z is 0.9030 c. The area between -z and z is 0.2052 d. The area to the left of z is 0.9948 e. The area to the right of z is 0.6915

a. -0.80 b. 1.66 c. 0.26 d. 2.56 e. -0.5

A university found that 40% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. If you compute the binomial probabilities manually, make sure to carry at least four decimal digits in your calculations. a. Compute the probability that 2 or fewer will withdraw (to 4 decimals). b. Compute the probability that exactly 4 will withdraw (to 4 decimals). c. Compute the probability that more than 3 will withdraw (to 4 decimals). d. Compute the expected number of will withdraw (to 4 decimals).

a. 0.0036 b. 0.0350 c. 0.9840 d. 8

The Food Marketing Institute shows that 15% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.15 and a sample of 800 households will be selected from the population. Use z-table. a. Calculate 𝞂(p), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals) b. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion (to 4 decimals)? c. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion for a sample of 1,800 households (to 4 decimals)?

a. 0.0126 b. 0.8882 c. 0.9826

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. Use Table 1 in Appendix B. a. What is the probability of completing the exam in one hour or less (to 4 decimals)? b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)? c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time? (to the next whole number)

a. 0.0228 b. 0.2857 c. 10

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): Critical Reading 502 Mathematics 515 Writing 494 Assume that the population standard deviation on each part of the test is 𝞂 = 100. Use z-table. a. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)? b. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)? c. What is the probability a sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 494 on the writing part of the test (to 4 decimals)?

a. 0.6578 b. 0.6878 c. 0.6827

Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of 2014, Google's Chrome browser exceeded a 20% market share for the first time, with a 20.37% share of the browser market (Forbes website, December 15, 2014). For a randomly selected group of 20 Internet browser users, answer the following questions. a. Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser (to 4 decimals). For this question, if you compute the probability manually, make sure to carry at least six decimal digits in your calculations. b. Compute the probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser (to 4 decimals). c. For the sample of 20 Internet browser users, compute the expected number of Chrome users (to 3 decimals). d. For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users (to 3 decimals).

a. 0.0243 b. 0.8050 c. 4.074 d. Variance - 3.2441 Standard Deviation - 1.8011

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. a. The probability of a player weighing more than 241.25 pounds is... b. The probability of a player weighing less than 250 pounds is... c. What percent of players weigh between 180 and 220 pounds?

a. 0.0495 b. 0.9772 c. 57.62%

The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $120. Use Table 1 in Appendix B. a. What is the probability that a domestic airfare is $555 or more (to 4 decimals)? b. What is the probability that a domestic airfare is $240 or less (to 4 decimals)? c. What is the probability that a domestic airfare is between $310 and $510 (to 4 decimals)? d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar)

a. 0.0783 b. 0.1135 c. 0.5852 d. $581.80 or more

Consider a binomial experiment with n = 20 and p = .70. If you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals) c. Compute P(x ≥ 16) (to 4 decimals). d. Compute P(x ≤ 15 ) (to 4 decimals). e. Compute E(x). f. Compute Var(x) (to 1 decimal) and 𝞂 (to 2 decimals)

a. 0.1144 b. 0.1304 c. 0.2374 d. 0.7625 e. 14 f. Var(x) - 4.2 𝞂 - 2.05

Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals). Use Table 1 in Appendix B. a. P(z ≤ -1.0) b. P(z ≥ -1.0) c. P(z ≥ -1.5) d. P(z ≥ -2.5) e. P(-3 < z ≤ 0)

a. 0.1587 b. 0.8413 c. 0.9332 d. 0.9938 e. 0.4986

Automobile repair costs continue to rise with the average cost now at $367 per repair (U.S. News & World Report website, January 5, 2015). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. Answer the following questions about the cost of automobile repairs. Use Table 1 in Appendix B. a. What is the probability that the cost will be more than $450 (to 4 decimals)? b. What is the probability that the cost will be less than $250 (to 4 decimals)? c. What is the probability that the cost will be between $250 and $450 (to 4 decimals)? d. If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost (to 2 decimals)?

a. 0.1728 b. 0.0918 c. 0.7354 d. $222.25

A salesperson contacts 10 potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is .10. a. What is the probability the salesperson will make exactly two sales in a day? b. What is the probability the salesperson will make at least two sales in a day? c. What percentage of days will the salesperson not make a sale? d. What is the expected number of sales per day? e. What is the standard deviation of sales?

a. 0.193 b. 0.2639 c. 0.348 d. 1 e. 0.949

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,000 and $15,400. a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)? b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)? c. What amount should you bid to maximize the probability that you get the property (in dollars)? d(a). Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13,000. If your objective is to maximize the expected profit, what is your bid? d(b). What is the expected profit for this bid (in dollars)?

a. 0.38 b. 0.74 c. 15400 d(a). Bid $13000 to maximize the expected profit d(b). $1680

The assembly time for a product is uniformly distributed between 6 to 10 minutes. a. The probability of assembling the product between 7 to 9 minutes is... b. The probability of assembling the product in less than 6 minutes is... c. The probability of assembling the product in 7 minutes or more is... d. The expected assembly time (in minutes) is...

a. 0.5 b. 0 c. 0.75 d. 8

A population proportion is .40. A sample of size 200 will be taken and the sample proportion will be used to estimate the population proportion. Use z-table. a. What is the probability that the sample proportion will be within ±.03 of the population proportion? (Round z value in intermediate calculations to 2 decimal places.) b. What is the probability that the sample proportion will be within ±.05 of the population proportion? (Round z value in intermediate calculations to 2 decimal places.)

a. 0.6156 b. 0.8516

Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 2 to 4 carpets. The production levels and their respective probabilities are shown below. Production Per Month Probability x f(x) 2 0.20 3 0.60 4 0.20 a. Refer to Exhibit 5-13. The standard deviation for the production is... b. Refer to Exhibit 5-13. The expected monthly production level is...

a. 0.63 b. 3.00

Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals). Use Table 1 in Appendix B. a. P(-1.98 ≤ z ≤ 0.49) b. P(0.52 ≤ z ≤ 1.22) c. P(-1.75 ≤ z ≤ -1.04)

a. 0.6641 b. 0.1902 c. 0.1091

One of the questions in the Pew Internet & American Life Project asked adults if they used the Internet at least occasionally (Pew website, October 23, 2012). The results showed that 454 out of 478 adults aged 18 - 29 answered Yes; 741 out of 833 adults aged 30 - 49 answered Yes; 1058 out of 1644 adults aged 50 and over answered Yes. Use z-table. a. Develop a point estimate of the proportion of adults aged 18 - 29 who use the Internet. b. Develop a point estimate of the proportion of adults aged 30 - 49 who use the Internet. c. Develop a point estimate of the proportion of adults aged 50 and over who use the Internet. d. Comment on any relationship between age and internet use that seems apparent. e. Suppose your target population of interest is that of all adults (18 years of age and over). Develop an estimate of the proportion of that population who use the Internet.

a. 0.9498 b. 0.8896 c. 0.6436 d. Younger adults are more likely to use the Internet e. 0.7624

Exhibit 1 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee/Frequency 0/700 1/900 2/600 3/300 -/2500 a. Refer to Exhibit 1. The expected number of cups of coffee is... b. Refer to Exhibit 1. The variance of the number of cups of coffee is....

a. 1.2 b. 0.96

Suppose a random sample of size 50 is selected from a population with 𝞂 = 11. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite (to 2 decimals) b. The population size is N = 50,000 (to 2 decimals). c. The population size is N = 5,000 (to 2 decimals). d. The population size is N = 500 (to 2 decimals).

a. 1.56 b. 1.56 c. 1.54 d. 1.48

The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied). Job Satisfaction Scores / IS Senior Executives / IS Middle Managers 1 / 0.05 / 0.04 2 / 0.09 / 0.10 3 / 0.03 / 0.12 4 / 0.42 / 0.46 5 / 0.41 / 0.28 a. What is the expected value of the job satisfaction score for senior executives (to 2 decimals)? b. What is the expected value of the job satisfaction score for middle managers (to 2 decimals)? c. Compute the variance of job satisfaction scores for executives and middle managers (to 2 decimals). d. Compute the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals). e. What comparison can you make about the job satisfaction of senior executives and middle managers?

a. 4.05 b. 3.84 c. Executive - 1.25 Middles Manager - 1.13 d. Executive - 1.12 Middles Manager - 1.06 e. Senior executives have higher satisfaction with more variations.

The following table provides a probability distribution for the random variable x. x /f(x) 3/0.25 6/0.50 9/0.25 a. Compute E(x), the expected value of x b. Compute 𝞂2, (variance) of x (to 1 decimal). c. Compute 𝞂, (standard deviation) of x (to 2 decimals).

a. 6 b. 4.5 c. 2.12

The National Football League (NFL) polls fans to develop a rating for each football game. Each game is rated on a scale from 0 (forgettable) to 100 (memorable). The fan ratings for a random sample of 12 games follow. 56 60 87 73 73 72 21 57 80 80 84 75 a. Develop a point estimate of mean fan rating for the population of NFL games (to 2 decimals). b. Develop a point estimate of the standard deviation for the population of NFL games (to 4 decimals).

a. 68.17 b. 17.9840

A sample of 5 months of sales data provided the following information: Month 1 2 3 4 5 Units Sold 94 100 85 94 92 a. Develop a point estimate of the population mean number of units sold per month. b. Develop a point estimate of the population standard deviation (to 2 decimals).

a. 93 b. 5.39

Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. a. Which of the following graphs accurately represent the probability density function for the flight time? b. What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? c. What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? d. What is the expected flight time, in minutes?

a. Graph 1 b. 0.5 c. 0.25 d. 130

A random variable is normally distributed with a mean of 𝝁 = 50 and a standard deviation of 𝞼 = 5. Use Table 1 in Appendix B. a. Which of the following graphs accurately represent the probability density function? b. What is the probability the random variable will assume a value between 45 and 55 (to 4 decimals)? c. What is the probability the random variable will assume a value between 40 and 60 (to 4 decimals)?

a. Graph 1 b. 0.6826 c. 0.9544

According to a 2013 study by the Pew Research Center, 15% of adults in the United States do not use the Internet (Pew Research Center website, December, 15, 2014). Suppose that 10 adults in the United States are selected randomly. a. Is the selection of the 10 adults a binomial experiment? b. What is the probability that all of the adults use the internet (to 4 decimals)? c. What is the probability that 3 of the adults do not use the Internet (to 4 decimals)? If you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations. d. What is the probability that at least 1 of the adults do not use the Internet (to 4 decimals)?

a. Yes b. 0.1969 c. 0.1298 d. 0.8031

The probability that a continuous random variable takes any specific value

is equal to zero

A negative value of Z indicates that

the number of standard deviations of an observation is to the left of the mean

Which of the following is a required condition for a discrete probability function?

∑f(x) = 1 For All Values of x