Deck 6: Discrete Probability Distributions

Question 1

In a Poisson distribution, the probability of success may vary from trial to trial.

Answer 1

False

Question 2

To construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial.

Answer 2

True

Question 3

The binomial probability distribution is always negatively skewed.

Answer 3

False

Question 4

To construct a binomial probability distribution, the mean must be known.

Question 5

The mean of a binomial distribution is the product of n and π.

Question 6

The mean of a probability distribution is called its expected value.

Question 7

The variance of a binomial distribution is found by nπ(1 - π).

Question 8

When sampling is done without replacement and the outcomes are measured as either a success or failure, the hypergeometric distribution should be applied.

Question 9

Judging from recent experience, 5% of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?

A) 0.001
B) 0.167
C) 0.735
D) 0.500

Question 10

The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.) for service is: On a typical day, how many automobiles should Lakeside Olds expect to be lined up at opening time?

A) 10.00
B) 1.00
C) 2.85
D) 1.96

Question 11

On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?

A) 0.002
B) 0.344
C) 0.599
D) 0.100

Question 12

The probability of a particular outcome must always be between 0.0 and 1.0 inclusive.

Question 13

A random variable represents the outcome of an experiment.

Question 14

If the variance is 3.6 grams, what is the standard deviation?

A) 0.600
B) 1.897
C) 6.000
D) 12.96

Question 15

A probability distribution is a mutually exclusive and collectively exhaustive listing of experimental outcomes that can occur by chance, and their corresponding probabilities.

Question 16

The variance of a probability distribution is based on the sum or squared differences from the mean.

Question 17

A total of 60% of the customers of a fast food chain order a hamburger, French fries, and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

A) 1.000
B) 0.186
C) 0.403
D) 0.000

Question 18

As a general rule of thumb, if the items selected for a sample are not replaced and the sample size is less than 5 percent of the population, the binomial distribution can be used to approximate the hypergeometric distribution.

Question 19

The variance measures the skewness of a probability distribution.

Question 20

The random variable for a Poisson probability distribution can assume an infinite number of values.

Question 21

A machine shop has 100 drill presses and other machines in constant use. The probability that a machine will become inoperative during a given day is 0.002. During some days, no machines are inoperative, but on other days, one, two, three, or more are broken down. What is the probability that fewer than two machines will be inoperative during a particular day?

A) 0.0200
B) 0.1637
C) 0.8187
D) 0.9824

Question 22

A manufacturer of headache medicine claims it is 70% effective within a few minutes. That is, out of every 100 users, 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that eight have relief within a few minutes?

A) 0.001
B) 0.168
C) 0.667
D) 0.231

Question 23

Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?

A) 0.8187
B) 0.2500
C) 0.0164
D) 0.0001

Question 24

Which of the following is correct about a probability distribution?

A) The sum of all possible outcomes must equal 1.0.
B) The outcomes must be mutually exclusive.
C) The probability of each outcome must be between 0.0 and 1.0 inclusive.
D) All apply.

Question 25

In a large metropolitan area, past records revealed that 30% of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?

A) 0.114
B) 0.887
C) 0.400
D) 0.231

Question 26

A listing of all possible outcomes of an experiment and their corresponding probabilities of occurrence is called a ____________.

A) random variable
B) probability distribution
C) subjective probability
D) frequency distribution

Question 27

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

A) 0.500
B) 0.125
C) 0.875
D) 0.000

Question 28

A true/false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?

A) 0
B) 0.016
C) 0.062
D) 0.250

Question 29

What kind of distributions are the binomial and Poisson probability distributions?

A) Discrete
B) Continuous
C) Both discrete and continuous
D) Neither discrete or continuous

Question 30

Which shape describes a Poisson distribution?

A) Positively skewed
B) Negatively skewed
C) Symmetrical
D) All apply

Question 31

Sponsors of a local charity decided to attract wealthy patrons to its $500-a-plate dinner by allowing each patron to buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50-50. If you bought 20 tickets, what is the chance of winning 15 or more prizes?

A) 0.250
B) 0.021
C) 0.006
D) 0.750

Question 32

A coin is tossed four times. The following table summarizes the experiment. What is the following table called?

A) Probability distribution
B) Cumulative frequency distribution
C) Standard deviation
D) Frequency table

Question 33

Which one of the following is NOT a condition of the binomial distribution?

A) Independent trials
B) Only two outcomes
C) The probability of success remains constant from trial to trial
D) Sampling at least 10 trials

Question 34

Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10% of the diamond wedding rings are returned. Five different customers buy a wedding ring. What is the probability that none of the customers return a ring?

A) 0.250
B) 0.073
C) 0.590
D) 0.500

Question 35

A farmer who grows genetically engineered corn is experiencing trouble with corn borers. A random check of 5,000 ears revealed the following: Many of the ears contained no borers. Some ears had one borer; A few had two borers, and so on. The distribution of the number of borers per ear approximated the Poisson distribution. The farmer counted 3,500 borers in the 5,000 ears. What is the probability that an ear of corn selected at random will contain no borers?

A) 0.3476
B) 0.4966
C) 1.000
D) 0.0631

Question 36

Chances are 50-50 that a newborn baby will be a girl. For families with five children, what is the probability that all the children are girls?

A) 0.900
B) 0.031
C) 0.001
D) 0.250

Question 37

The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsightly blemishes often appear because of improper mixture or other problems. A worker counted the number of blemishes on each door. Most doors had no blemishes; a few had one; a very few had two; and so on. The average number was 0.5 per door. The distribution of blemishes followed the Poisson distribution. Out of 10,000 doors painted, about how many would have no blemishes?

A) About 6,065
B) About 3,935
C) About 5,000
D) About 500

Question 38

Data show that the weight of an offensive linesman may be any weight between 200 and 350 pounds. The distribution of weight is based on a ______________.

A) continuous random variable
B) discrete random variable
C) qualitative variable
D) All apply.

Question 39

Which is true for a binomial distribution?

A) There are ten or more possible outcomes.
B) The probability of success remains the same from trial to trial.
C) The value of π is equal to 1.50.
D) It approximates the Poisson distribution.

Question 40

A new car was put into production. It involved many assembly tasks. Each car was inspected at the end of the assembly line and the number of defects per unit was recorded. For the first 100 cars produced, there were 40 defective cars. Some of the cars had no defects, a few had one defect, and so on. The distribution of defects followed a Poisson distribution. Based on the first 100 cars produced, about how many out of every 1,000 cars assembled should have one or more defects?

A) About 660
B) About 165
C) About 630
D) About 330

Question 41

What is the only variable in the Poisson probability formula?

A) π
B) x
C) e
D) P

Question 42

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have no messages?

A) 0.0067
B) Zero
C) 0.0335
D) Impossible to have no messages

Question 43

Which of the following is NOT a characteristic of a binomial probability distribution?

A) Each outcome is mutually exclusive.
B) Each trial is independent.
C) The probability of success remains constant from trial to trial.
D) The number of trials is limited to two.

Question 44

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have two messages?

A) 0.0067
B) 0.0014
C) 0.4200
D) 0.0842

Question 45

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that at least 10 pay in cash?

A) 0.024
B) 0.033
C) 0.009
D) 0.976

Question 46

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. This situation is an example of what type of discrete probability distribution?

A) Continuous probability distribution
B) Poisson probability distribution
C) Binomial probability distribution
D) Hypergeometric probability distribution

Question 47

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that all 15 pay in cash?

A) 0.0
B) 0.1
C) 0.9
D) 1.0

Question 48

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. Given the probability distribution, which of the following predictions is correct?

A) 60% of the employees will have more than one day absent per month.
B) There is a 0.04 probability that an employee will be absent one day per month.
C) There is a 0.12 probability that an employee will be absent two days per month.
D) There is a 0.50 probability that an employee will be absent 0.72 days per month.

Question 49

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. What is the variance of the number of days absent?

A) 1.1616
B) 1.41
C) 5.00
D) 55.52

Question 50

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. What is the standard deviation of the number of days absent?

A) 1.1616
B) 0
C) 1.6595
D) 1.0778

Question 51

For the following distribution: What is the variance of the distribution?

A) 1.1616
B) 0.964
C) 0.982
D) 1.000

Question 52

To apply a Poisson probability distribution, the mean can be computed as __________.

A) nπ
B)
C) e^-x
D)

Question 53

In a Poisson distribution, the variance is equal to ___________.

A) nπ
B)
C) e^-x
D)

Question 54

For the following distribution: What is the mean of the distribution?

A) 1
B) 2.5
C) 1.604
D) 3

Question 55

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages?

A) 0.0067
B) 0.8750
C) 0.1755
D) 1.0000

Question 56

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. What is the mode of the distribution?

A) 0.72 days
B) 2.5 days
C) 0 days
D) 3 days

Question 57

What must you know to develop a binomial probability distribution?

A) The probability of success
B) The probability of success and the number of trials
C) The probability of success and the number of successes
D) The number of trials and the number of successes

Question 58

For the following distribution: What is the mean of the distribution?

A) 2.1
B) 1.5
C) 0.441
D) 2

Question 59

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that more than 8 and less than 12 customers pay in cash?

A) 0.210
B) 0.212
C) 0.092
D) 0.562

Question 60

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. What is the mean number of days absent?

A) 1.00
B) 0.40
C) 0.72
D) 2.5

Question 61

The mean or expected value for a binomial probability distribution is _________.

A) μ = nπ(1 - π)
B) μ = π(1 - π)
C) μ = πn(1 - n)
D) μ = nπ

Question 62

Which of the following is a requirement for use of the hypergeometric distribution?

A) Only two possible outcomes
B) Trials are independent
C) Probability of a success is greater than 1.0
D) Sampling with replacement

Question 63

The following is a binomial probability distribution with n = 3 and π = 0.20. The mean of the distribution is _______.

A) 1.50
B) 0.60
C) 0.25
D) 0.00

Question 64

The following is a binomial probability distribution with n = 3 and π = 0.20. The variance of the distribution is _________.

A) 1.5
B) 3.0
C) 0.69
D) 0.48

Question 65

For the following distribution: What is the variance of the distribution?

A) 2.1
B) 0.63
C) 3.9
D) 2.754

Question 66

An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?

A) 0.250
B) 0.500
C) 0.410
D) 0.026

Question 67

For a trial, the number of possible outcomes for the binomial experiment is _____.

Question 68

Affirmative action commitments by many organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives that it will fill from among four women and six men. What is the probability that at least one woman is selected?

A) 8/15
B) 3/5
C) 2/3
D) 3/4

Question 69

The following is a Poisson probability distribution with µ = 0.1. The mean of the distribution is _____.

A) 1.5
B) 0.1
C) 0.25
D) 1.0

Question 70

For the following distribution: What is the mean of the distribution?

A) 2.1
B) 1.13
C) 0.113
D) 1.5

Question 71

Affirmative action commitments by many organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives that it will fill from among four women and six men. What is the probability that no woman is selected?

A) 1/5
B) 1/3
C) 2/15
D) 8/15

Question 72

For the following distribution: What is the variance of the distribution?

A) 2.1
B) 0.132
C) 0.364
D) 1.000

Question 73

A measure of the long-run average value of a random variable used to represent the central location of a probability distribution is called a(n) _____________.

A) population variance
B) population standard deviation
C) expected value
D) coefficient of variation

Question 74

For a binomial distribution, the mean is 4.0 and n = 8. What is π for this distribution?

A) 0.5
B) 1.00
C) 4.0
D) 0.1

Question 75

In which of the following discrete distribution does the probability of a success vary from one trial to the next?

A) Binomial
B) Poisson
C) Hypergeometric
D) All of these.

Question 76

The marketing department of a nationally known cereal maker plans to conduct a national survey to find out whether or not consumers of flake cereals can distinguish one of their favorite flake cereals. To test the questionnaire and procedure to be used, eight persons were asked to cooperate in an experiment. Five very small bowls of flake cereals were placed in front of a person. The bowls were labeled A, B, C, D and

A) 0.168
B) 0.009
C) 0.788
D) 0.125
E) The person was informed that only one bowl contained his or her favorite flake cereal. Suppose that the eight persons in the experiment were unable to identify their favorite cereal and just guessed which bowl it was in. What is the probability that none of the eight guessed correctly?

Question 77

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

A) discrete random variable
B) continuous random variable
C) complex random variable
D) simplex random variable

Question 78

The following is a Poisson probability distribution with µ = 0.1. The variance of the distribution is ______.

A) 1.0
B) 0.9046
C) 3.0
D) 0.1

Question 79

For a binomial distribution, the mean is 0.6 and n = 2. What is π for this distribution?

A) 0.5
B) 1.00
C) 0.3
D) 0.1

Question 80

A type of probability distribution that shows the probability of x successes in n trials, where the probability of success remains the same from trial to trial, is referred to as a ___________.

A) hypergeometric probability distribution
B) uniform probability distribution
C) normal probability distribution
D) binomial probability distribution