# Quiz 6: Discrete Probability Distributions

Statistics

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Q 3Q 3

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

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Q 4Q 4

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

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Q 6Q 6

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

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Q 8Q 8

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

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Q 14Q 14

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

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Q 15Q 15

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

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Q 16Q 16

If the variance is 3.6 grams,what is the standard deviation?
A)0.600
B)1.897
C)6.000
D)12.96

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Multiple Choice

Q 17Q 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

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Q 18Q 18

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

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Multiple Choice

Q 19Q 19

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

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Multiple Choice

Q 20Q 20

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

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Multiple Choice

Q 21Q 21

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)0.0614
D)0.0001

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Q 22Q 22

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

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Q 23Q 23

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

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Multiple Choice

Q 24Q 24

Which is true for a binomial distribution?
A)There are 10 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.

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Q 25Q 25

Which shape describes a Poisson distribution?
A)Positively skewed
B)Negatively skewed
C)Symmetrical
D)All of these answers are correct.

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Q 26Q 26

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

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Q 27Q 27

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

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Q 28Q 28

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 of these answers are correct.

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Q 29Q 29

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 of these answers are correct.

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Q 30Q 30

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

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Q 31Q 31

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

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Q 32Q 32

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

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Multiple Choice

Q 33Q 33

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

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Multiple Choice

Q 34Q 34

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 mixtures 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

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Multiple Choice

Q 35Q 35

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

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Multiple Choice

Q 36Q 36

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

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Multiple Choice

Q 37Q 37

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

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Multiple Choice

Q 38Q 38

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

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Multiple Choice

Q 39Q 39

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

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Multiple Choice

Q 40Q 40

A coin is tossed three 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

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Q 42Q 42

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.

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Multiple Choice

Q 43Q 43

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

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Multiple Choice

Q 44Q 44

To apply a Poisson probability distribution,the mean can be computed as ________.
A)nπ
B)
C)e - x
D)

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Q 46Q 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. What is the probability that at least 10 pay in cash?
A)0.024
B)0.033
C)0.009
D)0.976

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Multiple Choice

Q 47Q 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

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Q 48Q 48

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

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Q 49Q 49

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

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Multiple Choice

Q 50Q 50

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)0
C)0.0335
D)Impossible to have no messages

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Multiple Choice

Q 51Q 51

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

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Multiple Choice

Q 52Q 52

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

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Multiple Choice

Q 53Q 53

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

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Multiple Choice

Q 54Q 54

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

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Q 55Q 55

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.

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Multiple Choice

Q 56Q 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

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Multiple Choice

Q 57Q 57

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

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Q 59Q 59

For the following distribution: What is the variance of the distribution?
A)1.1616
B)0.964
C)0.982
D)1.000

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Q 60Q 60

For the following distribution: What is the mean of the distribution?
A)2.1
B)1.5
C)0.441
D)2

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Q 61Q 61

For the following distribution: What is the variance of the distribution?
A)2.1
B)0.63
C)3.9
D)2.754

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Q 62Q 62

For the following distribution: What is the mean of the distribution?
A)2.1
B)1.13
C)0.113
D)1.5

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Q 63Q 63

For the following distribution: What is the variance of the distribution?
A)2.1
B)0.132
C)0.364
D)1.000

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Q 64Q 64

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

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Multiple Choice

Q 65Q 65

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

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Multiple Choice

Q 66Q 66

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

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Multiple Choice

Q 67Q 67

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

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Multiple Choice

Q 68Q 68

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

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Q 69Q 69

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

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Multiple Choice

Q 70Q 70

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 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?
A)0.168
B)0.009
C)0.788
D)0.125

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Multiple Choice

Q 71Q 71

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 one out of five. Using the rules of probability,what is the likelihood that the agent will sell a policy to three of the four prospective clients?
A)0.250
B)0.500
C)0.410
D)0.026

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Multiple Choice

Q 72Q 72

In which of the following discrete distributions does the probability of a success vary from one trial to the next?
A)Binomial
B)Poisson
C)Hypergeometric
D)All of these answers are correct.

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Multiple Choice

Q 73Q 73

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

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Multiple Choice

Q 74Q 74

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

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Multiple Choice

Q 75Q 75

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

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Multiple Choice

Q 76Q 76

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

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Multiple Choice

Q 77Q 77

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

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Multiple Choice

Q 78Q 78

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

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Multiple Choice

Q 79Q 79

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

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Multiple Choice