Deck 6: Discrete Probability Distributions

Question 1

Determine whether the random variable described is discrete or continuous. The length in seconds of a randomly-selected TV commercial

A) discrete
B) continuous

Answer 1

continuous

Question 2

The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. Find P(2 or fewer).

A) 0.65
B) 0.29
C) 0.35
D) 0.64

Answer 2

0.64

Question 3

Determine whether the table represents a discrete probability distribution.

A) Yes
B) No

Answer 3

No

Question 4

Determine whether the random variable described is discrete or continuous. The total value of a set of coins

A) discrete
B) continuous

Question 5

Determine whether the table represents a discrete probability distribution.

A) Yes
B) No

Question 6

Determine whether the table represents a discrete probability distribution.

A) No
B) Yes

Question 7

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find P(1 or more).

A) 0.63
B) 0.72
C) 0.28
D) 0.91

Question 8

Fill in the missing value so that the following table represents a probability distribution.

A) 0.25
B) 0.15
C) 0.09
D) 0

Question 9

The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution.

A) 2.12
B) 2.23
C) 4.48
D) 1.46

Question 10

A sample of 6,000 computer monitors are examined for stuck pixels. Of them, 4,074 have no stuck pixels, 1,153 have one stuck pixel, 462 have two stuck pixels, 226 have three stuck pixels, and 85
Have four stuck pixels. Let X be the number of stuck pixels of a monitor randomly sampled from
This population. Find the probability distribution of X.

A)
B)
C)
D)

Question 11

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the mean

A) 1.37
B) 0.71
C) 1.43
D) 0.84

Question 12

Determine whether the random variable described is discrete or continuous. The number of 3-point shots made in a basketball game

A) discrete
B) continuous

Question 13

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the standard deviation

A) 1.18
B) 1.29
C) 0.59
D) 0.77

Question 14

The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. Compute the mean

A) 0.36
B) 2.17
C) 0.17
D) 0.43

Question 15

The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. Find the probability that there are fewer than four people in line.

A) 0.18
B) 0.82
C) 0.11
D) 0.93

Question 16

A survey asked 870 people how many times per week they dine out at a restaurant. The results are presented in the following table. Consider the 870 people to be a population. Let X be the number of times per week a person dines out
For a person sampled at random from this population. Find the probability that a person dines out 4
Or more times per week.

A) 0.849
B) 0.151
C) 0.059
D) 0.611

Question 17

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find the probability that a family took at least 3 vacations last year.

A) 0.11
B) 0.09
C) 0.26
D) 0.89

Question 18

Determine whether the random variable described is discrete or continuous. The number of minutes you must wait in line at the grocery store

A) continuous
B) discrete

Question 19

Compute the mean of the random variable with the given discrete probability distribution.

A) 11.0
B) 121.5
C) 21
D) 17.5

Question 20

There are 4,000 undergraduates registered at a certain college. Of them, 364 are taking one course, 496 are taking two courses, 460 are taking three courses, 1,512 are taking four courses, 1,056 are
Taking five courses, and 112 are taking six courses. Let X be the number of courses taken by a
Student randomly sampled from this population. Find the probability distribution of X.

A)
B)
C)
D)

Question 21

A survey asked 805 people how many times per week they dine out at a restaurant. The results are presented in the following table. Consider the 805 people to be a population. Let X be the number of times per week a person dines out
For a person sampled at random from this population. Compute the standard deviation

A) 2.1
B) 1.5
C) 2.2
D) 1.9

Question 22

A student takes a true-false test that has 14 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(5)

A) 0.1222
B) 0.0001
C) 0.1833
D) 0.0611

Question 23

A coin is tossed 14 times. Let X be the number of heads obtained. Is this a binomial distribution, and if so, what is the number of trials?

A) Not binomial
B) Binomial, n = 14
C) Binomial, n = 2

Question 24

In the game of craps, two dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 11. The probability that you win is , and if you win, your profit is $15.
If you lose, you lose $1. What is the expected value of your profit?

A) $0.83
B) -$0.94
C) -$0.11
D) $0.11

Question 25

A coin is tossed until a head appears. Let X be the number of tosses. Is this a binomial distribution, and if so, what is the number of trials?

A) Not binomial
B) Binomial, n = X
C) Binomial, n = 2

Question 26

A die is rolled 11 times. Let X be the sum of the numbers obtained. Is this a binomial distribution, and if so, what is the number of trials?

A) Not binomial
B) Binomial, n = 6
C) Binomial, n = 11

Question 27

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p.
N = 15, p = 0.9, P(13 or more)

A) 0.9444
B) 0.5490
C) 0.1841
D) 0.8159

Question 28

An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.15 of a $20,000 loss, probability 0.1 of a $30,000 profit, probability 0.25 of a $40,000
Profit, and probability 0.5 of breaking even (a profit of $0). What is the expected value of the profit?

A) $22,500
B) $10,000
C) $16,000
D) $16,667

Question 29

An insurance company sells a one-year term life insurance policy to an 80-year-old woman. The woman pays a premium of $1000. If she dies within one year, the company will pay $18,500 to her
Beneficiary. According to the company's statistics department, the probability that an 80-year-old
Woman will be alive one year later is 0.9581. Find the expected value of the insurance company's
Profit.

A) -$224.85
B) $224.85
C) -$182.95
D) $182.95

Question 30

In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001.
What is the expected value of your profit?

A) $0.349
B) -$0.65
C) $2.50
D) $0.65

Question 31

A survey asked 808 people how many times per week they dine out at a restaurant. The results are presented in the following table. Consider the 808 people to be a population. Let X be the number of times per week a person dines out
For a person sampled at random from this population. Find the probability that a person does not
Dine out at all.

A) 0
B) 0.144
C) 0.285
D) 0.428

Question 32

An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.2 of a $15,000 loss, probability 0.15 of a $20,000 loss, probability 0.05 of a $40,000
Profit, and probability 0.6 of breaking even (a profit of $0). What is the expected value of the profit?

A) $11,000
B) $1,667
C) -$4,000
D) $8,000

Question 33

Ten students are chosen from a statistics class of 22 students. Let X be the number who got an "A" in the class.
Is this a binomial distribution, and if so, what is the number of trials?

A) Not binomial
B) Binomial, n = 10
C) Binomial, n = 12
D) Binomial, n = 22

Question 34

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p.
N = 15, p = 0.9, P(14)

A) 0.2288
B) 0.0000
C) 0.3432
D) 0.9000

Question 35

A student takes a true-false test that has 8 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(6 or more)

A) 0.3633
B) 0.6367
C) 0.0352
D) 0.1445

Question 36

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p.
N =8, p = 0.6, P(3 or fewer)

A) 0.8263
B) 0.0498
C) 0.1737
D) 0.4059

Question 37

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p.
N = 11, p = 0.7, P(Fewer than 4)

A) 0.9957
B) 0.0006
C) 0.0216
D) 0.0043

Question 38

A survey asked 818 people how many times per week they dine out at a restaurant. The results are presented in the following table. Consider the 818 people to be a population. Let X be the number of times per week a person dines out
For a person sampled at random from this population. Compute the mean

A) 1.5
B) 2.2
C) 2.3
D) 2.0

Question 39

A student takes a true-false test that has 13 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(Fewer than 4)

A) 0.8666
B) 0.1334
C) 0.0112
D) 0.0461

Question 40

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 40% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 12 adult dogs is studied.
What is the probability that exactly 3 of them weigh 65 lb or more?

A) 0.0125
B) 0.1419
C) 0.8581
D) 0.9875

Question 41

At an airport, 77% of recent flights have arrived on time. A sample of 11 flights is studied. What is the mean number of flights that are on time?

A) 1.95
B) 8.47
C) 2.53
D) 2.91

Question 42

It is estimated that 30% of households own a riding lawn mower. A sample of 18 households is studied. What is the probability that no more than 3 of these own a riding lawn mower?

A) 0.94
B) 0.1646
C) 0.8354
D) 0.0600

Question 43

It is estimated that 45% of households own a riding lawn mower. A sample of 15 households is studied. What is the probability that exactly 7 of these own a riding lawn mower?

A) 0.8353
B) 0.1647
C) 0.7987
D) 0.2013

Question 44

At an airport, 83% of recent flights have arrived on time. A sample of 12 flights is studied. What is the standard deviation of the number of flights that are on time?

A) 1.69
B) 9.96
C) 1.30
D) 0.38

Question 45

In a poll conducted by a survey firm, 75% of respondents said that their jobs were sometimes or always stressful. Nine workers are chosen at random. What is the probability that less than 4 of
Them find their jobs stressful?

A) 0.0100
B) 0.9900
C) 0.0489
D) 0.0389

Question 46

In a poll conducted by a survey firm, 73% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. What is the mean number of workers who
Find their job stressful?

A) 5.84
B) 1.58
C) 1.26
D) 2.16

Question 47

In a poll conducted by a survey firm, 82% of respondents said that their jobs were sometimes or always stressful. Eleven workers are chosen at random. What is the probability that more than 9 of
Them find their jobs stressful?

A) 0.3164
B) 0.3849
C) 0.6836
D) 0.6151

Question 48

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 16 adult dogs is studied.
What is the probability that no more than 3 of them weigh 65 lb or more?

A) 0.9719
B) 0.9934
C) 0.0066
D) 0.0281

Question 49

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 25% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 11 adult dogs is studied.
What is the mean number of dogs who weigh 65 lb or more?

A) 11
B) 2.0625
C) 2.75
D) 1.4361

Question 50

It is estimated that 40% of households own a riding lawn mower. A sample of 13 households is studied. What is the mean number of households who own a riding mower?

A) 3.12
B) 13
C) 1.7664
D) 5.2

Question 51

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 12 adult dogs is studied.
What is the probability that more than 9 of them weigh 65 lb or more?

A) 0.0079
B) 0.9644
C) 0.0356
D) 0.0011

Question 52

At an airport, 78% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that exactly 7 of them were on time.

A) 0.1358
B) 0.0014
C) 0.8642
D) 0.0030

Question 53

Determine the indicated probability for a Poisson random variable with the given values of

A) 0.0431
B) 0.2613
C) 0.9569
D) 0.3840

Question 54

In a poll conducted by a survey firm, 76% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. What is the standard deviation of the
Number of workers who find their jobs stressful?

A) 1.21
B) 0.43
C) 1.46
D) 2.47

Question 55

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 25% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 14 adult dogs is studied.
What is the standard deviation of the number of dogs who weigh 65 lb or more?

A) 3.5
B) 14
C) 1.6202
D) 2.625

Question 56

At an airport, 78% of recent flights have arrived on time. A sample of 14 flights is studied. Find the probability that more than 12 of them were on time.

A) 0.3761
B) 0.6239
C) 0.1527
D) 0.8473

Question 57

At an airport, 77% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that no more than 4 of them were on time.

A) 0.0039
B) 0.0046
C) 0.9954
D) 0.9961

Question 58

It is estimated that 35% of households own a riding lawn mower. A sample of 10 households is studied. What is the standard deviation of the number of households who own a riding lawn mower?

A) 3.5
B) 1.5083
C) 2.275
D) 10

Question 59

In a poll conducted by a survey firm, 84% of respondents said that their jobs were sometimes or always stressful. Ten workers are chosen at random. What is the probability that exactly 6 of them
Find their jobs stressful?

A) 0.0018
B) 0.0483
C) 0.9517
D) 0.0012

Question 60

It is estimated that 40% of households own a riding lawn mower. A sample of 13 households is studied. What is the probability that more than 10 of these own a riding lawn mower?

A) 0.0078
B) 0.9922
C) 0.0013
D) 0.0001

Question 61

Determine the indicated probability for a Poisson random variable with the given values of

A) 0.6469
B) 0.7141
C) 0.4936
D) 0.5064

Question 62

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find

A) 3.8
B) 2.8
C) 8
D) 4

Question 63

Determine the indicated probability for a Poisson random variable with the given values of

A) 0.3954
B) 0.6196
C) 0.3804
D) 0.2102

Question 64

The number of typographical errors in a document follows a Poisson distribution with a mean of 2 errors per page. Let X represent the number of errors on 3 pages. Find P(Less than 3).

A) 0.0620
B) 0.0174
C) 0.6767
D) 0.0595

Question 65

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 4 per milliliter. What is the probability that there will be
Exactly 8 bacteria in a 4-milliliter sample?

A) 0.0298
B) 0.0120
C) 0.0060
D) 0.9940

Question 66

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 2 per milliliter. Find the standard deviation of the number of
Bacteria in a 4-milliliter sample.

A) 8
B) 1.4
C) 2.8
D) 2

Question 67

The number of typographical errors in a document follows a Poisson distribution with a mean of 2 errors per page. Let X represent the number of errors on 4 pages. Find P(5).

A) 0.1221
B) 0.0916
C) 0.9639
D) 0.0361

Question 68

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find

A) 4
B) 9
C) 8
D) 2.8

Question 69

The number of typographical errors in a document follows a Poisson distribution with a mean of 2 errors per page. Let X represent the number of errors on 4 pages. Find P(Greater than 1).

A) 0.5940
B) 0.9862
C) 0.9970
D) 0.9997

Question 70

Last year, a manufacturer produced 200,000 DVD players. Of these, approximately 2% were defective. Assume that a simple random sample of n = 130 players is drawn. Use the Poisson
Approximation to the binomial distribution to compute the mean number of DVD players that were
Defective.

A) 2.6
B) 25.1
C) 2
D) 1.6

Question 71

Last year, a manufacturer produced 1,950,000 DVD players. Of these, approximately 5% were defective. Assume that a simple random sample of n = 230 players is drawn. Use the Poisson
Approximation to the binomial distribution to compute the probability that exactly nineteen of the
230 DVD players were defective.

A) 0.0119
B) 0.0826
C) 0.0068
D) 0.0196

Question 72

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 6 per milliliter. Find the mean number of bacteria in a
8-milliliter sample.

A) 2.4
B) 48
C) 6.9
D) 6

Question 73

Last year, a manufacturer produced 350,000 DVD players. Of these, approximately 1% were defective. Assume that a simple random sample of n = 140 players is drawn. Use the Poisson
Approximation to the binomial distribution to compute the standard deviation of the number of DVD
Players that were defective.

A) 1
B) 1.4
C) 48.3
D) 1.2

Question 74

Determine the indicated probability for a Poisson random variable with the given values of

A) 0.9592
B) 0.0408
C) 0.8288
D) 0.6201

Question 75

Last year, a manufacturer produced 1,950,000 DVD players. Of these, approximately 4% were defective. Assume that a simple random sample of n = 180 players is drawn. Use the Poisson
Approximation to the binomial distribution to compute the probability that fewer than four of the
180 DVD players were defective.

A) 0.0464
B) 0.0255
C) 0.0719
D) 0.0712

Question 76

Determine the indicated probability for a Poisson random variable with the given values of

A) 0.4335
B) 0.4152
C) 0.5665
D) 0.2381