Deck 5: Discrete Probability Distributions

Question 1

The expected value of a discrete random variable is the average value for the random variable over many repeats of the experiment.

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

The standard deviation of a discrete probability distribution is the positive square root of the variance, which determines the expected value of the distribution.

Question 5

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

Question 6

A probability distribution identifies the probabilities that are assigned to all possible values of a random variable.

Question 7

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

Question 8

The first step in producing a probability distribution is to identify values for the random variable.

Question 9

The mean of a discrete probability distribution is generally referred to as the expected value of the distribution.

Question 10

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.

Question 11

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.

Question 12

One of the conditions for a binomial experiment is that the trials are statistically independent.

Question 13

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.

Question 14

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.

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

When playing a round of golf, the number of pars is considered to be a discrete variable.

Question 20

When playing a round of golf, the distance of the drive off the second tee in feet is considered to be a discrete variable.

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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.

Question 26

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.

Question 27

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

Question 28

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

Question 29

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

Question 30

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.

Question 31

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

Question 32

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

Question 33

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.

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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

Question 39

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.

Question 40

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

Question 41

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)

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

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

Question 57

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

Question 58

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)

Question 59

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

Question 60

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

Question 61

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

Question 62

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

A).1472
B).1588
C).1723
D).3129
E).2365

Question 63

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

Question 64

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

A).5989
B).7341
C).7944
D).8116
E).8328

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

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

Question 70

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

Question 71

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

Question 72

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

Question 73

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

Question 74

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

Question 75

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

A).0100
B).0467
C).0217
D).0952
E).1361

Question 76

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

Question 77

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

Question 78

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

Question 79

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

Question 80

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