Deck 4: Discrete Random Variables and Probability Distributions

Question 1

Which of the following is true about a probability distribution?

A)The sum of all possible outcomes must not equal 1.
B)The representation must be graphed,not tabular or algebraic.
C)The probability of each outcome must be between 0 and 1,inclusive.
D)The outcomes do not need to be mutually exclusive.

Answer 1

The probability of each outcome must be between 0 and 1,inclusive.

Question 2

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,you receive 2.6 pieces of junk mail a day.Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution.
What is the probability of receiving more than three pieces of junk mail today?

A)0.123
B)0.264
C)0.482
D)0.242

Answer 2

0.264

Question 3

The probability distribution function can be represented in a graph once the probabilities have been:

A)calculated.
B)ordered.
C)alphabetized.
D)journalized.

Answer 3

calculated.

Question 4

What is the standard deviation for the number of people catching a cold?

A)1.549
B)1.245
C)1.265
D)1.125

Question 5

The expected value of a random variable,denoted μ,is also called its:

A)mode.
B)median.
C)mean.
D)variance.

Question 6

Consider the following probability distribution.Which of the following is true?

A)P(2 < X < 5)= 0.42
B)P(X > 6)= 0.07
C)P(X ≥ 3)= 0.64
D)P(X ≤ 6)= 0.93

Question 7

The approach,to develop the binomial probability distribution,begins with the:

A)Bayes' theorem.
B)Empirical rule.
C)Venn diagram.
D)Bernoulli model.

Question 8

If the outcomes of a discrete random variable follow a Poisson distribution,then their:

A)mean equals the standard deviation.
B)mean equals the variance.
C)median equals the variance.
D)median equals the standard deviation.

Question 9

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The probability that a person catches a cold during the cold and flu season is 0.4.Assume that 10 people are chosen at random.
What is the probability that exactly four of them will catch a cold?

A)0.7502
B)0.6330
C)0.3670
D)0.2508

Question 10

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,you receive 2.6 pieces of junk mail a day.Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution.
What is the expected number of pieces of junk mail you receive daily?

A)6.76
B)1.61
C)3.22
D)2.60

Question 11

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,you receive 2.6 pieces of junk mail a day.Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution.
What is the standard deviation of the number of pieces of junk mail you receive daily?

A)1.61
B)2.60
C)6.76
D)There is not sufficient information to determine this.

Question 12

The Poisson distribution can be used to approximate the binomial probabilities when the number of trials n is large and at the same time the probability P is:

A)also large.
B)one.
C)small.
D)equal to λ.

Question 13

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The probability that a person catches a cold during the cold and flu season is 0.4.Assume that 10 people are chosen at random.
What is the probability that four or more of them will catch a cold?

A)0.715
B)0.618
C)0.546
D)0.312

Question 14

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,you receive 2.6 pieces of junk mail a day.Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution.
What is the probability that you receive exactly three pieces of junk mail today?

A)0.198
B)0.233
C)0.218
D)0.176

Question 15

Which of the following can be used to approximate the binomial distribution when the number of trials n is large and the probability of success P is small such that nP ≤ 7?

A)Poisson distribution
B)hypergeometric distribution
C)any discrete distribution
D)any distribution with a mean equals 7

Question 16

The standard deviation of a discrete random variable σ is the positive square root of its:

A)variance.
B)mean.
C)median.
D)mode.

Question 17

The probability of observing the specific sequence of discrete outcomes is arrived at by applying the:

A)Bayes' theorem.
B)multiplication rule of probabilities.
C)Hypergeometric distribution.
D)conditional rule of probabilities.

Question 18

A variable that can take on a finite and countable number of values is a ________ variable.

A)qualitative
B)discrete
C)continuous
D)Poisson

Question 19

On average,how many of these ten people would you expect to catch a cold?

A)4
B)3
C)2
D)1

Question 20

A random variable which takes on no more than a countable number of values is called a(n):

A)continuous random variable.
B)outcome.
C)statistic.
D)discrete random variable.

Question 21

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,there are 3.2 defects in a sheet of rolled steel.Assume that the number of defects follows a Poisson distribution.
What is the probability of having more than three defects in a roll?

A)0.354
B)0.398
C)0.412
D)0.621

Question 22

Thirty percent of all households have a DVD player.If you select 20 houses at random,what is the probability that six or fewer of them have a DVD player?

A)0.608
B)0.416
C)0.344
D)0.238

Question 23

The number of rainy days per month at Seattle follows a Poisson distribution with a mean value of 4.5 days.What is the probability that it will rain 3 days next month?

A)0.3604
B)0.2222
C)0.1687
D)0.2521

Question 24

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A basketball player makes 80 percent of his free throws during the regular season.Consider his next eight free throws.
What is the probability that he will make between four and six (inclusive)free throws?

A)0.1468
B)0.4863
C)0.4404
D)0.6291

Question 25

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,there are 3.2 defects in a sheet of rolled steel.Assume that the number of defects follows a Poisson distribution.
What is the probability of having exactly three defects in a roll?

A)0.412
B)0.223
C)0.318
D)0.335

Question 26

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees.
What is the probability that at least two of the trainees will still be employed at the end of nine months?

A)0.9841
B)0.0984
C)0.1143
D)0.0159

Question 27

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees.
What is the probability that three of the trainees will still be employed at the end of nine months?

A)0.0012
B)0.0146
C)0.0415
D)0.0446

Question 28

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees.
What is the standard deviation of the number of trainees that will still be employed at the end of nine months?

A)0.540
B)0.240
C)0.735
D)0.490

Question 29

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees.
What is the expected number of the trainees that will still be employed at the end of nine months?

A)0.6
B)0.9
C)3.0
D)4.0

Question 30

In a recent survey,70% of human resource directors thought that it was very important for business students to take a course in business ethics.For a sample of 12 human resource directors,what is the probability that at least one of them does not think it very important for business students to take a business ethics course?

A)0.9833
B)0.9521
C)0.9862
D)0.9714

Question 31

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A basketball player makes 80 percent of his free throws during the regular season.Consider his next eight free throws.
What is the probability that he will make at least six free throws?

A)0.1468
B)0.3355
C)0.7969
D)0.2936

Question 32

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees.
What is the probability that none of the trainees will still be employed at the end of nine months?

A)0.5314
B)0.3771
C)0.4686
D)0.0000

Question 33

Which of the following is an example of a discrete random variable?

A)The distance you can drive in a car with a full tank of gas.
B)The number of cows on a cattle ranch.
C)The weight of a package at the post office.
D)The amount of rain that falls over a 24-hour period.

Question 34

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A basketball player makes 80 percent of his free throws during the regular season.Consider his next eight free throws.
What is the standard deviation of the number of free throws that he will make?

A)1.131
B)1.280
C)2.608
D)2.828

Question 35

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A basketball player makes 80 percent of his free throws during the regular season.Consider his next eight free throws.
What is the probability that he will make exactly six free throws?

A)0.1468
B)0.3355
C)0.1678
D)0.2936

Question 36

When sampling without replacement from a finite population such that the probability of a success is no longer constant from trial to trial,the data must follow a:

A)binomial distribution.
B)Poisson distribution.
C)hypergeometric distribution.
D)continuous probability distribution.

Question 37

The sum of the product of each value of a discrete random variable X and its probability is referred to as its:

A)probability distribution.
B)expected value.
C)variance.
D)standard deviation.

Question 38

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees.
What is the probability that between one and three (inclusive)of the trainees will still be employed at the end of nine months?

A)0.3543
B)0.0984
C)0.0146
D)0.4673

Question 39

The finishing process on new furniture leaves slight blemishes.The table below displays a manager's probability assessment of the number of blemishes in the finish of new furniture.
On average,how many defects would we expect on a piece of furniture?

A)0.28
B)0.85
C)1.44
D)0.77

Question 40

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A basketball player makes 80 percent of his free throws during the regular season.Consider his next eight free throws.
What is the expected number of free throws that he will make?

A)6.4
B)6.0
C)5.0
D)4.0

Question 41

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The number of accidents on a particular highway averages 4.4 per year.Assume that the number of accidents follows a Poisson distribution.
A recent survey showed that 5 percent of the computer keyboards produced by a particular company are defective.What is the probability that out of eight keyboards selected at random,exactly zero keyboards will be defective?

A)0.0054
B)0.2793
C)0.6634
D)0.6983

Question 42

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The number of accidents on a particular highway averages 4.4 per year.Assume that the number of accidents follows a Poisson distribution.
What is the probability that there are more than three accidents next year?

A)0.389
B)0.440
C)0.512
D)0.641

Question 43

In a tennis match,a player must win three of five sets to win the match.If a player wins the first two sets,what is the probability that the player will win the match,assuming that each player is equally likely to win each set?

A)0.25
B)0.50
C)0.125
D)0.875

Question 44

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Consider the following probability distribution function.

What is the standard deviation of X?

A)13.25
B)3.64
C)1.62
D)4.13

Question 45

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Consider the following probability distribution function.

What is the expected value of X?

A)2.74
B)0.46
C)1.78
D)3.02

Question 46

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The number of accidents on a particular highway averages 4.4 per year.Assume that the number of accidents follows a Poisson distribution.
There are 15 professors in the School of Education.Twelve of them have received good evaluations from students,while 3 received poor evaluations.You will take three courses in the School of Education next semester.What is the probability that all of your professors next semester have received good evaluations?

A)0.516
B)0.484
C)0.258
D)0.242

Question 47

Consider the following probability distribution.Which of the following is true?

A)P(X > 3)= 0.51
B)P(2 ≤ X ≤ 5)= 0.33
C)P(X ≥3)= 0.51
D)P(X < 6)=1

Question 48

The number of orders shipped to a supplier that are inaccurate each month is an example of a:

A)discrete variable.
B)continuous variable.
C)binary variable.
D)hypergeometric variable.

Question 49

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In an office of 18 people,there are 7 men and 11 women.A subcommittee of four people will be formed from this group.
How many different ways can you select four people from a group of 18?

A)1,386
B)1,584
C)3,280
D)3,060

Question 50

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In an office of 18 people,there are 7 men and 11 women.A subcommittee of four people will be formed from this group.
What is the probability that the subcommittee contains two men and two women?

A)0.377
B)0.522
C)0.261
D)0.755

Question 51

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution.
In a box of 16 chocolates,there are four chocolates with coconut filling.What is the probability of choosing four chocolates,none of which have coconut fillings?

A)0.272
B)0.264
C)0.248
D)0.236

Question 52

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution.
The listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called a(n):

A)random variable.
B)objective probability.
C)probability distribution.
D)hypergeometric function.

Question 53

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution.
What is the probability that there are exactly four calls during the next ten minutes?

A)0.194
B)0.172
C)0.156
D)0.134

Question 54

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution.
What is the probability that there are three or fewer calls during the next ten minutes?

A)0.211
B)0.372
C)0.396
D)0.425

Question 55

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A cereal manufacturer produces a cereal that claims to contain 16 ounces in each box.A sample of boxes results in the following table.

What is the standard deviation of the weight of cereal in the boxes?

A)0.81
B)1.25
C)0.90
D)1.19

Question 56

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A cereal manufacturer produces a cereal that claims to contain 16 ounces in each box.A sample of boxes results in the following table.

What is the mean weight of the sample of cereal boxes?

A)15.5
B)15.7
C)16.0
D)16.5

Question 57

Which of the following is an example of a continuous random variable?

A)The number of cars in a parking lot.
B)The number of repairs at a computer shop over the course of the week.
C)The total points scored in a basketball game.
D)The weight of a bag of potatoes.

Question 58

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution.
It has been estimated that 30% of all farms are family-owned.In a sample of 12 farms,what is the probability that exactly three farms are family owned?

A)0.20
B)0.30
C)0.36
D)0.24

Question 59

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The number of accidents on a particular highway averages 4.4 per year.Assume that the number of accidents follows a Poisson distribution.
What is the probability that there are exactly four accidents next year?

A)0.504
B)0.192
C)0.375
D)0.286

Question 60

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Consider the following probability distribution function.

Which of the following is true for the binomial distribution?

A)There are at least three or more possible outcomes.
B)The probability of success remains the same for each trial.
C)The probability of success P,is equal to 1.99 most of the time.
D)The number of trials are not independent.

Question 61

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
70% of the customers at the local ice cream shop order their ice cream on a sugar cone.Assume that the next ten customers order independently of one another.
What is the probability that more than half of them order sugar cones?

A)0.95
B)0.85
C)0.05
D)0.15

Question 62

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A computer store receives a shipment of 14 computers,5 of which already have modems installed.Unfortunately,the boxes are not labeled so you are unsure which computers have modems.Assume you select 4 computers.
What is the probability that exactly two of them have modems?

A)0.3288
B)0.3704
C)0.3596
D)0.3012

Question 63

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.

What is the variance of the number of claims processed?

A)3.6211
B)2.0819
C)1.4428
D)1.9029

Question 64

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In a shipment of 18 trucks to a local truck dealer,there are four trucks that don't have air conditioning.Assume that you select four trucks at random.
What is the probability that two of the four don't have air conditioning?

A)0.121
B)0.145
C)0.178
D)0.212

Question 65

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.

There is a 50% chance that a newborn baby will be a boy.For families with four children,what is the probability that all the children are boys?

A)0.2512
B)0.3754
C)0.0625
D)0.1587

Question 66

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In a shipment of 18 trucks to a local truck dealer,there are four trucks that don't have air conditioning.Assume that you select four trucks at random.
In Detroit metropolitan area,past records revealed that only 20 percent of all the high school graduates go to college.From 20 graduates selected at random,what is the probability that exactly 5 will go to college?

A)0.2000
B)0.2054
C)0.2182
D)0.1746

Question 67

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.

Let a = -μ_x/σ_x and b = 1/σ_x in the linear function Z = a + bX.Which of the following statements is true?

A)μ_z = μ_x
B)μ_z = 0
C)σ_z = a + bσ_x
D)σ_z = σ_x

Question 68

A true-false quiz consists of ten questions.If you guess the answer to each question,what is the probability of getting all ten questions correct?

A)0.0010
B)0.0439
C)0.2051
D)0.2461

Question 69

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.

What is the average number of claims processed?

A)4.67
B)4.23
C)4.41
D)4.81

Question 70

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,an RV sales lot sells six RVs per month.Assume the number of sales of RVs per month follows the Poisson distribution.
What is the probability that exactly six RVs are sold next month?

A)0.266
B)0.508
C)0.232
D)0.161

Question 71

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.

Which of the following is true?

A)P(X > 4)= 0.46
B)P(X ≤ 4)= 0.27
C)P(X > 2)= 1.00
D)P(X ≥ 6)= 0.10

Question 72

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A recent survey found that 40% of all air traffic controllers found their job extremely stressful.Suppose 12 air traffic controllers are selected at random.
What is the probability that exactly 5 of them consider their job extremely stressful?

A)0.241
B)0.213
C)0.227
D)0.232

Question 73

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
70% of the customers at the local ice cream shop order their ice cream on a sugar cone.Assume that the next ten customers order independently of one another.
What is the probability that exactly seven of them order sugar cones?

A)0.2668
B)0.5000
C)0.6500
D)0.3500

Question 74

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A computer store receives a shipment of 14 computers,5 of which already have modems installed.Unfortunately,the boxes are not labeled so you are unsure which computers have modems.Assume you select 4 computers.
What is the probability that no more than two of them have modems?

A)0.802
B)0.871
C)0.834
D)0.905

Question 75

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
A recent survey found that 40% of all air traffic controllers found their job extremely stressful.Suppose 12 air traffic controllers are selected at random.
What is the probability that two or more of them consider their job extremely stressful?

A)0.7218
B)0.9804
C)0.0282
D)0.2806

Question 76

Which of the following statements regarding a binomial experiment is false,where n is the number of trials,and p is the probability of success in each trial?

A)The n trials are independent.
B)The standard deviation is np(1 - p).
C)The mean is np.
D)There are only two possible outcomes.

Question 77

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,an RV sales lot sells six RVs per month.Assume the number of sales of RVs per month follows the Poisson distribution.
What is the probability that more than three RVs are sold next month?

A)0.8488
B)0.7350
C)0.9826
D)0.7149

Question 78

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In a shipment of 18 trucks to a local truck dealer,there are four trucks that don't have air conditioning.Assume that you select four trucks at random.
What is the probability that two or fewer of the four don't have air conditioning?

A)0.7727
B)0.9814
C)0.8169
D)0.9242

Question 79

Which of the following is an example of a binomial experiment?

A)A shopping mall is interested in the income level of its customers and is taking a survey to gather information.
B)A business firm introducing a new product wants to know how many purchases its clients will make each year.
C)A sociologist is researching an area in an effort to determine the proportion of households with a male head of household.
D)A study is concerned with the average number of hours worked by high school students.

Question 80

Given that = 400,
= 625,Cov(X,Y)= 375,and n = 10,then the correlation coefficient is:

A)0.75
B)0.70
C)0.85
D)0.80