Test Bank Chapter 5 - Discrete Probability Distributions

CHAPTER 5

True/False

1. A description of how the probabilities are distributed over the values the random variable can assume is called a random variable.

1. When playing a round of golf, the distance of the drive off the second tee in feet is considered to be a discrete variable.
2. When playing a round of golf, the number of pars is considered to be a discrete variable.
3. A probability distribution identifies the probabilities that are assigned to all possible values of a random variable.
4. The first step in producing a probability distribution is to identify values for the random variable.
5. The symbol “x” is used to denote the random variable while the symbol “P(x)” is used to denote the probabilities associated with the random variable.
6. The mean of a discrete probability distribution is generally referred to as the expected value of the distribution.
7. The expected value of a discrete random variable is the average value for the random variable over many repeats of the experiment.

1. The expected value of a discrete random variable is the value of the random variable that occurs most frequently.

1. The standard deviation of a discrete probability distribution is the positive square root of the variance, which determines the expected value of the distribution.
2. One of the conditions for a binomial experiment is that the trials are statistically independent.

1. One of the conditions for a binomial experiment is that the probability of success on any one trial changes throughout the experiment.

1. In a binomial experiment x is always less than or equal to n, the number of trials.

1. The binomial probability function is composed of two parts, the second of which computes the probability of each of the ways in which the x successes in n trials can occur.
2. The binomial probability function is composed of two parts, the first of which computes the probability of each of the ways in which the x successes in n trials can occur.
3. One of the conditions for a Poisson experiment is that the average number of occurrences per unit of time, space, or distance is constant and proportionate to the size of the unit of time, space, or distance involved.

1. The expected value or mean of a Poisson distribution is the same as the variance.

MULTIPLE CHOICE

1. The number of customers that enter a store during one day is an example of:

a. a continuous random variable

b. a discrete random variable

c. either a continuous or a discrete random variable, depending on the number of the customers

d. either a continuous or a discrete random variable, depending on the gender of the customers

e. none of the above

1. The number of damaged items found on a shelf in a grocery store when taking inventory is:

a. a discrete random variable

b. a continuous random variable

c. either a continuous or a discrete random variable, depending on the number of the items found

d. either a continuous or a discrete random variable, depending on the type of item

e. a complex random variable

1. An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable is the number of sales made. This random variable is a:

a. a discrete random variable

b. a continuous random variable

c. either a continuous or a discrete random variable, depending on the number of the calls made

d. either a continuous or a discrete random variable, depending on the gender of the customers

e. a complex random variable

1. A discrete random variable would be an appropriate way to describe the outcome of which of the following experiments?

a. the color of car chosen by a randomly selected car buyer

b. the number of points a soccer team scores in its next game

c. the length of time it takes a randomly selected commuter to drive to work

d. the area of a city covered by trees

e. the distance covered by a golfer hitting the ball off the tee

1. If X is a discrete random variable,

a. it is possible for X to take on an infinite number of values.

b. X may only take a finite number of values.

c. X may only take on whole number values.

d. X cannot take on negative values.

e. X cannot take on positive values.

1. If Z represents the sum of two discrete random variables X and Y,

a. Z may be a discrete or a continuous random variable.

b. the probability distribution of Z is obtained by adding the distributions of X and Y.

c. Z may not satisfy the general requirements for a discrete probability distribution

d. Z will also be a discrete random variable.

e. Z will be a continuous random variable.

1. Which of the following is NOT a general requirement for a discrete probability distribution?

a. the random variable must take on whole-numbered values.

b. each probability must be greater than or equal to zero.

c. the sum of the probabilities of all values must be one.

d. the random variable must take on distinct numerical values.

e. each probability must be less than or equal to 1.

1. Which of the following is the second step involved in building a discrete probability distribution?

a. defining the random variable

b. identifying the values for the random variable

c. assigning probabilities to values of the random variable

d. building a bar chart of the distribution

e. calculating the expected value and variance

1. Which of the following is the first step involved in building a discrete probability distribution?

a. defining the random variable

b. identifying the values for the random variable

c. assigning probabilities to values of the random variable

d. building a bar chart of the distribution

e. calculating the expected value and variance

1. Which of the following is NOT one of the steps involved in building a discrete probability distribution?

a. defining the random variable

b. identifying the values for the random variable

c. assigning probabilities to values of the random variable

d. building a bar chart of the distribution

e. none of the above

1. The variance of a discrete random variable is a weighted average of the:

a. squared deviations from the mean

b. squared deviations from the median

c. square root of the deviations from the mean

d. square root of the deviations from the median

e. none of the above

1. A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial,

a. tails cannot appear

b. heads has a larger chance of appearing than tails

c. tails has a better chance of appearing than heads

d. heads and tails both have an equal chance of appearing

e. none of the above

1. Which of the following is a condition of a binomial experiment?

a. only two outcomes are possible on each of the trials

b. the trials are statistically independent

c. the probability of success remains constant throughout the experiment

d. all of the above

e. none of the above

1. Which of the following is NOT a condition of an experiment where the binomial probability distribution is applicable?

a. the experiment has a sequence of n identical trials

b. exactly two outcomes are possible on each trial

c. the trials are dependent

d. the probabilities of the outcomes do not change from one trial to another

e. all are characteristics of a binomial probability experiment

1. Which of the following is a condition for a binomial probability experiment?

a. the experiment involves a number of “trials,” represented by n.

b. only two outcomes are possible on each of the trials.

c. the trials are statistically independent.

d. the probability of success, p, on any one trial remains constant throughout the experiment.

e. all of the above

1. Which of the following best describes the logic of the binomial function?

a. the first part counts the number of ways in which exactly x successes in n trials can occur while the second part computes the probability of each of the ways in which the x successes can occur

b. the first part counts the number of ways in which exactly n successes in x trials can occur while the second part computes the probability of each of the ways in which the n successes can occur

c. the first part computes the probability of each of the ways in which the x successes can occur while the second part simply counts the number of ways in which exactly x successes in n trials can occur

d. the first part computes the probability of each of the ways in which the n successes can occur while the second part simply counts the number of ways in which exactly n successes in x trials can occur

e. none of the above

1. The variance of a binomial random variable X with n trials and p probability of success, where p is greater than 0,

a. will always be less than the expected value of X.

b. will always be equal to the expected value of X.

c. will always be greater than the expected value of X.

d. may be less than, equal to, or greater than the expected value of X.

e. has no relationship to the expected value of X.

1. Suppose a random variable X describes the outcome of a binomial experiment with 30 trials and a 0.80 probably of success for each trial. The shape of the distribution of X is:

a. negatively skewed

b. symmetric

c. positively skewed

d. bimodal

e. insufficient information is given to determine the distribution shape

1. The binominal distribution:

a. may be used to describe a discrete or a continuous random variable.

b. is used to describe a particular type of discrete random variable.

c. is a special case of the Poisson distribution.

d. may be used to describe any experiment whose outcome takes discrete values.

e. is only useful when dealing with distance, time, or space.

1. Which of the following is a condition for a Poisson probability experiment?

a. we need to be assessing the probability for the number of occurrences of some event per unit time, space, or distance.

b. the average number of occurrences per unit of time, space, or distance is constant.

c. the average number of occurrences per unit of time, space, or distance is proportionate to the size of the unit of time, space, or distance involved.

d. individual occurrences of the event are random and statistically independent.

e. all of the above

1. The expected value or mean of a Poisson distribution is equal to:

a. the variance of the distribution.

b. the standard deviation of the distribution.

c. the negative square root of the variance of the distribution.

d. the number of occurrences multiplied by its probability.

e. none of the above

1. Which graph below shows the shape of the Poisson distribution for λ = 5?

a. a

b. b

c. c

d. d

e. none of the above

FILL IN THE BLANK

1. A would be an appropriate way to describe the outcome of which of an experiments that involves the number of points a soccer team makes in its next game.

a. discrete random variable

b. continuous random variable

c. time-series random variable

d. exponential random variable

e. Poisson random variable

1. The step involved in building a discrete probability distribution is identifying the values for the random variable.

a. first

b. second

c. third

d. fourth

e. fifth

1. The calculations for the expected value (mean) and variance of a discrete probability distribution are essentially identical to those for a :

a. frequency distribution

b. percent frequency distribution

c. relative frequency distribution

d. binomial probability distribution

e. continuous probability distribution

1. The of a binomial distribution is equal to n time p.

a. expected value

b. variance

c. standard deviation

d. probability of success

e. the number of trials

1. One of the conditions for a Poisson experiment is the need to assess probability for the number of occurrences of some event per unit .

a. space

b. time

c. distance

d. space, time, or distance

e. space or time

PROBLEMS

1. The number of re-tweets of your Twitter tweets over the last ten days is shown below. If you define a random variable that counts the number of daily re-tweets during this 10-day period, show the possible values for the random variable in ascending order.

3, 1, 1, 0, 1, 1, 2, 2, 0, 2.

a. 0, 1, 2, 3

b. 1, 2, 3, 4

c. 1, 1, 0, 3

d. 2, 2, 1, 0

e. 0, 2, 3, 4

1. The number of re-tweets of your Twitter tweets over the last ten days is shown below. If you define a random variable that counts the number of daily re-tweets during this 10-day period, which set of probabilities would be used to form the probability distribution for this random variable?

3, 1, 1, 0, 1, 1, 2, 2, 0, 2.

a. .1, .3, .5, .1

b. .3, .4, .3, .1

c. .2, .1, .5, .2

d. .2, .4, .3, .1

e. .2, .2, .4, .2

1. The number of re-tweets of your Twitter tweets over the last ten days is shown below. If you pick a day at random, how likely is it that the number of re-tweets on that day is 2?

3, 1, 1, 0, 1, 1, 2, 2, 0, 2.

a. .10

b. .30

c. .20

d. .25

e. .40

1. Which one of the following probability distributions accurately represents the random variable “the number of times heads comes up in two tosses of a fair coin”?

a.

b.

c.

d.

e.

1. Which one of the following probability distributions represents the random variable “the number of 6’s that appear in a roll of two fair dice”?

a.

b.

c.

d.

e.

1. Hi-Plains Design is bidding on a project that will earn the company at least $650 million. The competitive bidding process will involve presenting the company’s proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains bid to be successful. If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel. If it is approved there, Hi-Plains will present the proposal to the third panel. Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages. Define “number of Hi-Plains presentations” as your random variable for this “experiment.” The possible values for the random variable (in ascending order) are:

a. 0,1,2,3

b. 1,2,3

c. 0,1,2,3,4

d. 1,2,3,4

e. 0,1

1. Hi-Plains Design is bidding on a project that will earn the company at least $650 million. The competitive bidding process will involve presenting the company’s proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains bid to be successful. If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel. If it is approved there, Hi-Plains will present the proposal to the third panel. Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages. Define “number of review panel approvals” as your random variable. The possible values for the random variable (in ascending order) are:

a. 1,2,3

b. 1,2,3,4

c. 0,1,2

d. 2,3,4

e. 0,1,2,3

1. Hi-Plains Design is bidding on a project that will earn the company at least $650 million. The competitive bidding process will involve presenting the company’s proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains’ bid to be successful. If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel. If it is approved there, Hi-Plains will present the proposal to the third panel. Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages. Define “number of panels that fail to approve the proposal” as your random variable. The possible values for the random variable (in ascending order) are:

a. 0,1,2,3

b. 1,2

c. 1,2,3,4

d. 0,1

e. 0,0,2,3

1. Hi-Plains Design is bidding on a project that will earn the company at least $650 million. The competitive bidding process will involve presenting the company’s proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains’ bid to be successful. If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel. If it is approved there, Hi-Plains will present the proposal to the third panel. Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages. Define “number of Hi-Plains presentations” as the random variable x. Which distribution below shows the proper probability distribution for this random variable?

a.

b.

c.

d.

a. a

b. b

c. c

d. d

e. none of the above

1. Hi-Plains Design is bidding on a project that will earn the company at least $650 million. The competitive bidding process will involve presenting the company’s proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains’ bid to be successful. If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel. If it is approved there, Hi-Plains will present the proposal to the third panel. Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages. Define “number of approvals” as the random variable x. Which distribution below shows the proper probability distribution for this random variable?

a.

b.

c.

d.

a. a

b. b

c. c

d. d

e. None of them

1. Hi-Plains Design is bidding on a project that will earn the company at least $650 million. The competitive bidding process will involve presenting the company’s proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains’ bid to be successful. If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel. If it is approved there, Hi-Plains will present the proposal to the third panel. Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages. If you define “number of panels that fail to approve” as the random variable x, which distribution below shows the proper probability distribution for this random variable?

a.

b.

c.

d.

a. a

b. b

c. c

d. d

e. none of the above

1. Seven percent of the potential customers visiting Gadget.com’s website make at least one purchase: 4% purchase item A, 5% purchase item B, and 2% percent purchase both. If you define “number of items purchased by a website visitor” as a random variable, the possible values for the random variable are, in ascending order,

a. 1,2,3

b. 2,4,5

c. 0,1,2

d. 1,1,1

e. 3,2,1

1. Seven percent of the potential customers visiting Gadget.com’s website make at least one purchase: 4% purchase item A, 5% purchase item B, and 2% percent purchase both. If you define “number of items purchased by a website visitor” as a random variable, which set of probabilities would be used to form the probability distribution for this random variable?

a. .63, .25, .12

b. .82, .12, .05

c. .93, .05, .02

d. .83, .14, .03

e. .12, .23, .65

1. You need to buy three books for your finance course this semester. You estimate that there is 60% chance of that you can buy any one of the books cheaper online than in the bookstore. If you define “number of the finance books that will be cheaper online” as a random variable, the possible values for the random variable are, in ascending order:

a. 1,2,3,4

b. 0,1,2

c. 2,4,6

d. 0,1,2,3

e. 4,3,2,1

1. You need to buy three books for your finance course this semester. You estimate that there is 60% chance of that you can buy any one of the books cheaper online than in the bookstore. If you define “number of the finance books that will be cheaper online” as a random variable, which set of probabilities would be used to form the probability distribution for this random variable?

a. .064, .298, .422, .216

b. .064, .288, .432, .216

c. .064, .268, .452, .216

d. .064, .238, .482, .216

e. .238, .064, .216, .482

1. Below is a table showing the probability distribution for the random variable x. Compute the expected value of the random variable.

a. 36.4

b. 35.0

c. 32.9

d. 41.3

e. 38.0

1. Below is a table showing the probability distribution for the random variable x. Compute the variance of the random variable.

a. 84.2

b. 72.0

c. 54.2

d. 64.0

e. 95. 9

1. Below is a table showing the probability distribution for the random variable x. Compute the standard deviation of the random variable.

a. 8.49

b. 14.63

c. 8.00

d. 3.85

e. 23.56

1. The following probability distribution represents the number of vehicles available for use by a randomly selected US household. To simplify matters, the category “three or more” is replaced by “3” (Source: US Census, American FactFinder). Calculate the expected value of the number of vehicles available per household.

a. 0.25

b. 0.42

c. 1.50

d. 1.66

e. 2.50

1. The following probability distribution represents the number of vehicles available for use by a randomly selected US household. To simplify matters, the category “three or more” is replaced by “3” (Source: US Census, American FactFinder). Calculate the standard deviation of the number of vehicles available per household.

a. 0.11

b. 0.79

c. 0.89

d. 1.12

e. 1.45

1. The following probability distribution represents the number of bedrooms in a randomly selected US household. To simplify matters, the category “five or more” is replaced by “5” (Source: US Census, American FactFinder). Calculate the expected value of the number of bedrooms per household.

a. 0.17

b. 0.54

c. 2.50

d. 2.68

e. 3.65

1. The following probability distribution represents the number of bedrooms in a randomly selected US household. To simplify matters, the category “five or more” is replaced by “5” (Source: US Census, American FactFinder). Calculate the variance of the number of bedrooms per household.

a. 0.017

b. 1.070

c. 1.145

d. 2.917

e. 3.215

1. Julian picks winning and losing stocks by tossing a coin (heads means winner, tails means loser).To test his ‘system’, his friend gives him a list of 20 stocks, half of which doubled in value over the past 3 years (winners) and half of which lost half their value over the past 3 years (losers). How likely is it that Julian properly classifies at least 60% of the stocks on the list?

a. .2202

b. .1786

c. .1365

d. .1973

e. .2517

1. Julian picks winning and losing stocks by tossing a coin (heads means winner, tails means loser).To test his ‘system’, his friend gives him a list of 20 stocks, half of which doubled in value over the past 3 years (winners) and half of which lost half their value over the past 3 years (losers). How likely is it that Julian properly classifies at least 80% of the stocks on the list?

a. .0201

b. .0059

c. .1201

d. .0952

e. .1028

1. Approximately 1% of all USPS package deliveries are lost. You select 10 deliveries at random. Assuming that all the binomial conditions are met, what is the “expected” number of lost packages in this 10 delivery sample?

a. 1.00

b. .1542

c. .0666

d. .100

e. .0914

1. Approximately 1% of all USPS package deliveries are lost. You select 10 package deliveries at random. If you use the binomial probability function to compute the probability that none of the packages is lost, the value of the binomial coefficient in your computation is

a. .9900

b. .0100

c. 10.00

d. .9044

e. 1.00

1. Approximately 1% of all USPS package deliveries are lost. You select 10 package deliveries at random. Use the binomial probability function to compute the probability that no more than one package will be lost.

a. .8753

b. .9958

c. .9044

d. .8842

e. .9562

1. It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners. If you scratch 250 tickets, what is the expected number of winners?

a. 19.8

b. 22.6

c. 17.5

d. 27.4

e. 29.1

1. It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners. If you scratch 250 tickets what is the variance of the random variable “number of winners”?

a. 12.5

b. 11.9

c. 16.3

d. 14.8

e. 9.9

1. It is reported that 7% of the Super Star scratch-and-win lottery tickets are winners. If you scratch 250 tickets, what is the standard deviation of the random variable “number of winning tickets”?

a. 4.03

b. 5.12

c. 4.62

d. 3.98

e. 5.53

1. It is reported that 23% of the home mortgages in Cowlitz County are “underwater”. For 50 randomly selected home mortgages, compute the expected number of underwater mortgages.

a. 12.9

b. 14.2

c. 9.6

d. 10.1

e. 11.5

1. It is reported that 23% of the home mortgages in Cowlitz County are “underwater”. For 50 randomly selected home mortgages, compute the variance of the random variable “number of underwater mortgages.”

a. 9.12

b. 8.86

c. 16.23

d. 12.47

e. 11.58

1. It is reported that 23% of the home mortgages in Cowlitz County are “underwater”. For 50 randomly selected home mortgages, compute the standard deviation of the random variable “number of underwater home mortgages” in the sample of 50. Assume all the binomial conditions are met.

a. 3.66

b. 4.38

c. 1.33

d. 2.98

e. 1.80

1. Five percent of all international video calls on Interphone.com are dropped. Suppose you randomly choose 5 recent calls. If you use the binomial function to compute the probability that exactly 3 of the 5 calls are dropped, what is the value of the binomial coefficient in you computation?

a. .0458

b. 5.0

c. 10.0

d. .0011

e. 2.0

1. Five percent of all international video calls on Interphone.com are dropped. Suppose you randomly choose 5 recent calls. Use the binomial function to compute the probability that none of the calls are dropped.

a. .6234

b. .5612

c. .8945

d. .6432

e. .7738

1. Five percent of all international video calls on Interphone.com are dropped. Suppose you randomly choose 5 recent calls. Use the binomial function to compute the probability that no more than two calls are dropped.

a. .9988

b. .7613

c. .8234

d. .6736

e. .4431

1. For a binomial distribution, find P(x = 2), where n = 8, p = .7.

a. .0100

b. .0467

c. .0217

d. .0952

e. .1361

1. For a binomial distribution, find P(3 < x < 5), where n = 15, p = .5.

a. .1472

b. .1588

c. .1723

d. .3129

e. .2365

1. For a binomial distribution, find P(x > 2), where n = 10, p = .4.

a. .5989

b. .7341

c. .7944

d. .8116

e. .8328

1. Use the Binomial distribution to produce P(x < 12), where n = 15, p = .7.

a. .7821

b. .6631

c. .5978

d. .8116

e. .8732

1. Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization. You interview 30 randomly selected graduating seniors. Assuming that all the binomial conditions are met, determine the probability that exactly one student in this group of 30 plans to volunteer.

a. .2234

b. .1775

c. .1612

d. .1413

e. .2972

1. Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization. You interview 30 randomly selected graduating seniors. Assuming that all the binomial conditions are met, determine the probability that at least three students in the group plan to volunteer.

a. .4889

b. .5886

c. .6214

d. ,6652

e. .4116

1. Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization. You interview 30 randomly selected graduating seniors. Assuming that all the binomial conditions are met, determine the probability that no more than 4 students in the group plan to volunteer.

a. .7663

b. .8598

c. .8246

d. .8916

e. .9113

1. Ten percent of graduating college seniors report planning to spend at least one year volunteering for a charitable organization. You interview 30 randomly selected graduating seniors. Assuming that all the binomial conditions are met, determine the probability that between 2 and 5 students in the group plan to volunteer.

a. .5219

b. .7432

c. .7873

d. .8226

e. .6482

1. Your car (like most cars) has four tires. Each tire has a 1% chance of running low on air in the morning. Assume that the state of one tire has no relationship to the state of the others. Use the binomial probability function to determine the probability that one tire will be running low on air tomorrow morning.

a. 0.010

b. 0.039

c. 0.250

d. 0.999

e. 0.450

1. Your car (like most cars) has four tires. Each tire has a 5% chance of running low on air in the morning. Assume that the state of one tire has no relationship to the state of the others. Use the binomial probability function to determine the probability that no more than one tire will be running low on air tomorrow morning.

a. 0.171

b. 0.814

c. 0.900

d. 0.986

e. 0.450

1. The most popular names for babies born in the United Kingdom in 2012 were Harry and Amelia. Of the roughly 400,000 baby boys born in the UK in 2012, two percent were named Harry. Two percent of girls born in the UK in 2012 were named Amelia (Source: UK Office for National Statistics, Baby Names, England and Wales, 2012). If thirty boys are selected at random from those born in the UK in 2012, what is the probability that two boys or more in the group will be named Harry?

a. 9.9%

b. 12.1%

c. 54.5%

d. 87.9%

e. 93.2%

1. The most popular names for babies born in the United Kingdom in 2012 were Harry and Amelia. Of the roughly 400,000 baby boys born in the UK in 2012, two percent were named Harry, while two percent of the girls born that year were named Amelia (Source: UK Office for National Statistics, Baby Names, England and Wales, 2012). Suppose that 30 baby girls are chosen at random. Let X represent the number of girls named Amelia. What is the expected value of X?

a. 0.02

b. 0.06

c. 1.00

d. 2.00

e. 3.45

1. The most popular names for babies born in the United Kingdom in 2012 were Harry and Amelia. Of the roughly 400,000 baby boys born in the UK in 2012, two percent were named Harry, while two percent of the girls born that year were named Amelia (Source: UK Office for National Statistics, Baby Names, England and Wales, 2012). Suppose that 20 baby boys are chosen at random. Let X represent the number of boys named Harry. What is the standard deviation of X?

a. 4.472

b. 0.179

c. 0.040

d. 0.032

e. 1.360

1. Salem University’s MBA program has a 55% acceptance rate. If you randomly select a sample of 20 applicants, how likely is it that 10 of the applicants will be accepted into the program?

a. .1315

b. .1987

c. .1593

d. .1823

e. .1772

1. Salem University’s MBA program has a 55% acceptance rate. If you randomly select a sample of 20 applicants, how likely is it that no more than five of the applicants in the sample will fail to be accepted into the program?

a. .0162

b. .1083

c. .0002

d. .0553

e. .0241

1. Salem University’s MBA program has a 55% acceptance rate. If you randomly select a sample of 20 applicants, how likely is it that between 13 and 17 (inclusive) of the applicants will be accepted into the program?

a. .2989

b. .3196

c. .3341

d. .2511

e. .2813

1. Salem University’s MBA program has a 55% acceptance rate. You randomly select a sample of 20 applicants. For the random variable "number of applicants in the sample who are accepted into the program,” compute the expected value.

a. 11

b. 12.2

c. 9.8

d. 7.4

e. 13.5

1. Salem University’s MBA program has a 55% acceptance rate. You randomly select a sample of 20 applicants. For the random variable "number of applicants in the sample who are accepted into the program,” compute the standard deviation.

a. 3.88

b. 1.22

c. 2.98

d. 2.23

e. 3.45

1. In recent years, 30% of the patent applications submitted to the US Patent Office have been approved. Assuming that this same rate holds in the future, if 15 new applications are submitted this year, how likely is it that at least 9 of them will be disapproved?

a. .9093

b. .8689

c. .1311

d. .0907

e. .9455

1. In recent years, 30% of the patent applications submitted to the US Patent Office have been approved. Assuming that this same rate holds in the future, if 15 new applications are submitted this year, how likely is it that between 11 and 13 (inclusive) applications will be disapproved?

a. .4093

b. .4802

c. .5198

d. .3557

e. .6455

1. 80% of surviving tech startups still aren’t making a profit after three years. If you track twenty startups three years after they began operations, how likely is it that six or more of them are making a profit?

a. .2347

b. .3172

c. .3418

d. .2561

e. .1958

1. 80% of surviving tech startups still aren’t making a profit after three years. If you track twenty startups three years after they began operations, how likely is it that more than 8 will be making a profit?

a. .003

b. .2010

c. .0100

d. .0074

e. .0990

1. 80% of surviving tech startups still aren’t making a profit after three years. In a sample of twenty startups that have survived for at least three years, there’s less than a 5% chance that more than what number are making a profit.

a. 7

b. 3

c. 5

d. 2

e. 6

1. Car Sounds sells and installs high-end sound systems for cars. 10% of the systems that the company installs need to be re-installed because of faulty first-time installation. You plan to randomly select 20 of Car Sounds’ recent installations. How likely is it that at least three of these systems will require re-installation.?

a. .3230

b. .3732

c. .2554

d. .1989

e .2868

1. Car Sounds sells and installs high-end sound systems for cars. 10% of the systems that the company installs need to be re-installed because of faulty first-time installation. You plan to randomly select 20 of Car Sounds’ recent installations. How likely is it that the company will have to re-install no more than one of these systems?

a. .2671

b. .3416

c. .2956

d. .3687

e. .3918

1. Car Sounds sells and installs high-end sound systems for cars. 10% of the systems that the company installs need to be re-installed because of faulty first-time installation. You plan to randomly select 20 of Car Sounds’ recent installations. In this sample, there’s less than a 2% chance that more than what number of the systems will have to be re-installed.

a. 5

b. 4

c. 6

d. 3

e. 10

1. You plan to randomly select 10 city restaurants. Historically, 70% of city restaurants are rated “high pass” by city health inspectors. If this percentage is still true, determine the probability that among the ten restaurants you select you’ll find exactly two that have been rated “high pass.”

a. .0120

b. .1003

c. .0651

d. .0014

e. .0102

1. You plan to randomly select 10 city restaurants. Historically, 70% of city restaurants are rated “high pass” by city health inspectors. If this percentage is still true, determine the probability that among the ten restaurants you select, fewer than three are not rated “high pass.”

a. .4767

b. .2997

c. .3246

d. .3178

e. .3828

1. You plan to randomly select 10 city restaurants. Historically, 70% of city restaurants are rated “high pass” by city health inspectors. If this percentage is still true, determine the probability that among the ten restaurants you select, between 4 and 7 are rated “high pass.”

a. .6066

b. .6975

c. .7853

d. .8110

e. .7724

1. Use the Poisson probability function to find P(x = 3), where λ= 7.

a. .6072

b. .7113

c. .5021

d. .4329

e. .4789

1. Use the Poisson probability function to find P(x = 1), where λ = 1.3.

a. .2564

b. .3829

c. .3381

d. .4607

e. .3543

1. Use the Poisson probability function to find P(1 < x< 3), where λ = 3.2.

a. .3478

b. .5617

c. .4213

d. .3897

e. .4536

1. Use the Poisson probability function to find P(x < 3), where λ = 1.

a. .7643

b. .9197

c. .8872

d. .9750

e. .9562

1. Use the Poisson probability function to find P(x = 4), where λ= 3.

a. .1123

b. .2240

c. .1680

d. .2631

e. .0902

1. Use the Poisson probability function to find P(x > 13), where λ = 5.

a. .0002

b. .0004

c. .0200

d. .0168

e. .0001

1. Use the Poisson probability function to find P(3 < x < 5), where λ = 2.

a. .2497

b. .3067

c. .1961

d. .1789

e. .4282

1. In an ordinary 8-hour day, Roto-Drains receives calls for emergency service at an average rate of 1 per hour (otherwise, the calls appear to be random and independent). The owner currently has a crew of technicians capable of handling up to (and including) nine emergencies per day. What is the probability that on a random day there are more calls than her crew can handle?

a. .2833

b. .2617

c. .3419

d. .2509

e. .2864

1. In an ordinary 8-hour day, Roto-Drains receives calls for emergency service at an average rate of 1 per hour (otherwise, the calls appear to be random and independent). The owner currently has a crew of technicians capable of handling up to (and including) nine emergencies per day. She is considering expanding the crew. If she wants to ensure that there is less than a 5% chance that the crew won't be able to handle the emergency load, she will need a crew that can handle up to (and including) how many emergencies per day.

a. 13

b. 12

c. 15

d. 11

e. 10

1. On average stoppages on the assembly line at Jamari Industries have a Poisson distribution with a mean of .1 per hour. Use the Poisson probability function to determine the probability of having exactly two stoppages in a 10-hour period.

a. .2462

b. .2884

c. .3462

d. .1839

e. .2163

1. On average stoppages on the assembly line at Jamari Industries have a Poisson distribution with a mean of .1 per hour. Use the Poisson probability function to determine the probability of having no stoppages in a 20 hour period.

a. .0986

b. .1025

c. .0878

d. .1226

e. .1353

1. On average stoppages on the assembly line at Jamari Industries have a Poisson distribution with a mean of .1 per hour. Use the Poisson probability function to determine the probability of having no more than one stoppage in a 30-hour period.

a. .1992

b. .1689

c. .1364

d. .2567

e. .1043

1. On average stoppages on the assembly line at Jamari Industries have a Poisson distribution with a mean of .1 per hour. Assume all the Poisson conditions are met. Use the Poisson probability function to determine the probability of having at least two stoppages in a 15-hour period.

a. .3265

b. .4422

c. .5123

d. .6213

e. .4746

1. During a meteor shower, ‘shooting stars’ occur at an average rate of 12 per minute or .2 per second. Assume all the Poisson conditions are met. What is the probability of exactly one ‘shooting star’ in a randomly selected second?

a. .2136

b. .2653

c. .1918

d. .1637

e. .3157

1. During a meteor shower, ‘shooting stars’ occur at an average rate of 12 per minute or .2 per second. Assume all the Poisson conditions are met. What is the probability of no more than two ‘shooting stars’ in a particular second?

a. .8823

b. .7642

c. .9988

d. .9087

e. .8346

1. During a meteor shower, ‘shooting stars’ occur at an average rate of 12 per minute or .2 per second. Assume all the Poisson conditions are met. What is the probability of exactly three ‘shooting stars’ in a randomly selected half-minute?

a. .1346

b. .0502

c. .1654

d. .1997

e. .0892

1. During a meteor shower, ‘shooting stars’ occur at an average rate of 12 per minute or .2 per second. Assume all the Poisson conditions are met. What is the probability of between one and three ‘shooting stars’ in a 20-second time interval?

a. .4152

b. .2587

c. .3216

d. .3762

e. .4585

1. In a study of NBA basketball games, it was reported that there are, on average, .3 fouls committed per minute. Assume all the Poisson conditions are met. Determine the probability of exactly one foul in a randomly selected minute.

a. .1111

b. .2222

c. .3671

d. .1438

e. .2789

1. In a study of NBA basketball games, it was reported that there are, on average, .3 fouls committed per minute. Assume all the Poisson conditions are met. Determine the probability of no fouls in a randomly selected 2-minute interval.

a. .6783

b. .7221

c. .6109

d. .5834

e. .5488

1. In a study of NBA basketball games, it was reported that there are, on average, .3 fouls committed per minute. Assume all the Poisson conditions are met. Determine the probability of more than 2 fouls in a randomly selected 4-minute interval.

a. .1766

b. .0942

c. .0561

d. .1203

e. .0783

1. In a study of NBA basketball games, it was reported that there are, on average, .3 fouls committed per minute. Assume all the Poisson conditions are met. You are watching a game. Determine the probability of five fouls in the next 10-minute interval.

a. .1257

b. .1008

c. .2090

d. .1368

e. .1552

1. On average, 2.3 wind turbines at the vast Kindler Range Wind Farm malfunction and need repair. Assume that all the Poisson conditions are met. Letting x represent values of the random variable “number of turbines that malfunction during any one day,” determine the probability that x = 2.

a. .1578

b. .2652

c. .2231

d. .3472

e. .3225

1. The average number of wind turbines at the vast Kindler Range Wind Farm that malfunction and need repair is 2.3 per day. Assume that all the Poisson conditions are met. Letting x represent values of the random variable “number of turbines that malfunction during any one day,” what is the expected value of x?

a. 4.2

b. 3.6

c. 1.9

d. 2.9

e. 2.3

1. The average number of wind turbines at the vast Kindler Range Wind Farm that malfunction and need repair is 2.3 per day. Assume that all the Poisson conditions are met. Letting x represent values of the random variable “number of turbines that malfunction during any one day,” what is the variance of x?

a. 2.3

b. 3.5

c. 2.9

d. 3.3

e. 4.7

1. During the summer season, the average number of lightning strikes per week in the Royal Canyon area is 3.6. Assume that all the Poisson conditions are met. Let x represent values for the random variable “number of lightning strikes in a week.” What is the expected value of x?

a. 4.6

b. 5.1

c. 4.2

d. 3.6

e. 4.9

1. During the summer season, the average number of lightning strikes per week in the Royal Canyon area is 3.6. Assume that all the Poisson conditions are met. Let x represent values for the random variable “number of lightning strikes in a week.” What is the variance of x?

a. 4.9

b. 5.2

c. 2.7

d. 3.0

e. 3.6

1. During the summer season, the average number of lightning strikes per week in the Royal Canyon area is 3.6. Assume that all the Poisson conditions are met. Let x represent values for the random variable “number of lightning strikes in a week.” What is the standard deviation of x?

a. 1.897

b. 2.354

c. 4.162

d. 1.212

e. 1.318

1. Requests for a chat with a customer service representative on Maximax.com’s website conform roughly to the Poisson conditions. The average number of requests is six per hour. Compute the probability of exactly four requests during the next hour.

a. .0968

b. .1123

c. .0792

d. .1339

e. .1024

1. Requests for a chat with a customer service representative on MaxTrend.com’s website conform roughly to the Poisson conditions. The average number of requests is six per hour. Compute the probability of at least 10 requests during the next hour.

a. .0557

b. .0838

c. .1126

d. .1487

e. .2232

1. Requests for a chat with a customer service representative on MaxTrend.com’s website conform roughly to the Poisson conditions. The average number of requests is six per hour. Compute the probability of no more than one request during the next hour and a half.

a. .0012

b. .0200

c. .0317

d. .1017

e. .0120

1. Requests for a chat with a customer service representative on MaxTrend.com’s website conform roughly to the Poisson conditions. The average number of requests is six per hour. Compute the probability of exactly two requests during the next thirty minutes.

a. .2240

b. .2617

c. .3419

d. .2509

e. .2864

1. Requests for a chat with a customer service representative on MaxTrend.com’s website conform roughly to the Poisson conditions. The average number of requests is six per hour. The probability is approximately 6% that fewer than what number of requests will be made in the next hour.

a. 5

b. 2

c. 9

d. 4

e. 3

1. At work, Serge receives an average of four e-mails every hour. Assuming that all of the Poisson conditions are met, use the Poisson probability function to calculate the probability that Serge receives no e-mails in the next hour.

a. 0%

b. 2%

c. 18%

d. 25%

e. 44%

1. At work, Serge receives an average of four e-mails every hour. Assuming that all of the Poisson conditions are met, use the Poisson probability function to calculate the probability that Serge receives no e-mails in the next 15 minutes.

a. 1%

b. 2%

c. 25%

d. 37%

e. 48%

1. The binomial probability for P(x = 5), where n = 20, p =.1 is .0319. If you use the Poisson distribution to approximate this binomial probability, what probability would you produce?

a. .0918

b. .0361

c. .0117

d. .0266

e. .0141

1. The binomial probability for P(x < 2), where n = 18, p = .05 is .9418. If you use the Poisson distribution to approximate this binomial probability, what probability would you produce?

a. .7656

b. .8146

c. .9372

d. .9514

e. .9716

1. The binomial probability for P(1 < x < 3), where n = 30, p = .01 is .2601. If you use the Poisson distribution to approximate this binomial probability, what probability would you produce?

a. .1775

b. .1413

c. .2588

d. .2263

e. .1917

1. Use the Poisson distribution to approximate the binomial probability P(x = 2) when n = 200, p = .03.

a. .0201

b. .0838

c. .0446

d. .1098

e. .1286

1. Use the Poisson distribution to approximate the binomial probability P(x = 4) when n = 1000, p = .001.

a. .0617

b. .0992

c. .0234

d. .1182

e. .0153

1. Use the Poisson distribution to approximate the binomial probability P(x < 2) when n = 800, p = .002 .

a. .6658

b. .5864

c. .4392

d. .7833

e. .5246

1. Use the Poisson distribution to approximate the binomial probability, P(x = 7), where n = 100, p = .04

a. .0782

b. .1213

c. .0595

d. .0994

e. .1390