Deck 6: Discrete Probability Distributions

Question 1

To construct a binomial probability distribution,the number of trials and the probability of success must be known.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

A random variable may be either discrete or continuous.

Answer 3

True

Question 4

A Poisson distribution is a discrete probability distribution.It has the same four characteristics as the binomial,but in addition,the probability of a success is small and the number of trials is relatively large.

Question 5

A discrete variable may assume fractional or decimal values,but they must have distance between them.

Question 6

A random variable is assigned nominal or numerical values based on the outcomes of an experiment.

Question 7

A random variable represents the outcomes of an experiment.

Question 8

The Poisson probability distribution is a continuous probability distribution.

Question 9

If we toss two coins and count the number of heads,there could be 0,1 or 2 heads.The number of heads resulting from this experiment is a random variable.

Question 10

The Poisson probability distribution is always negatively skewed.

Question 11

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

Question 12

If Unique Buying Services has 100 employees,there might be 0,or 1,or 2,or 3,or up to 100 employees absent on Monday.In this case,the day of the week is the random variable.

Question 13

The probability of a particular outcome must always be between 0 and 100 inclusive.

Question 14

For a binomial distribution,outcomes of an experiment are classified into one of two mutually exclusive categories (a success or a failure).

Question 15

For a binomial distribution,each trial has a known number of successes.For example,a four question multiple-choice test can only have zero,one,two,three and four successes (number correct).

Question 16

A binomial distribution has a characteristic that the trials are independent,which means that the outcome of one trial does not affect the outcome of any other trial.

Question 17

A discrete random variable can have only certain clearly separated values.

Question 18

If we measure the weight of a car,the variable is a discrete random variable.

Question 19

For a binomial distribution,the probability of a success stays the same for each trial,but the probability of a failure varies from trial to trial.

Question 20

For a binomial distribution,the data collected are the result of counts.

Question 21

The mean of a binomial probability distribution can be determined by multiplying the probability of a failure by the number of trials.

Question 22

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

A)Random variable
B)Probability distribution
C)Subjective probability
D)Frequency distribution

Question 23

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

Question 24

Which is true for a binomial distribution?

A)There are three or more possible outcomes.
B)Probability of success remains the same from trial to trial.
C)Value of p is equal to 1.50.
D)It approximates the Poisson distribution.

Question 25

The binomial and Poisson distributions are discrete probability distributions.

Question 26

If the probability of success ( $\pi$ )remains the same,but n increases,the shape of the binomial distribution becomes more symmetrical.

Question 27

The variance of a binomial distribution is found by $\eta$ $\pi$ (1 - $\pi$ ).

Question 28

The mean of a binomial distribution is the product of n and $\pi$ .

Question 29

Judging from recent experience,5 percent 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 30

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

Question 31

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

A)Independent trials
B)Only two outcomes
C)Probability of success remains constant from trial to trial
D)At least 10 observations

Question 32

A mail-order house,advertising "same day" service,received a large number of complaints.A change in the handling of orders was made with less than 5 unfilled orders on hand (per picker)at the end of 95 out of every 100 working days.Frequent checks of unfilled orders at the end of the day revealed that the distribution of unfilled orders approximated a Poisson distribution;that is,most of the days there were no unfilled orders;some of the days there was one order,and so on.Since the average number of unfilled orders per picker was 2.0,the mail-order house lived up to its goal.

Question 33

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

A)0.6
B)1.897
C)6.0
D)12.96

Question 34

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

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

Question 35

On a very hot summer day,5 percent 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 36

The binomial probability distribution is always negatively skewed.

Question 37

A binomial distribution is a continuous probability distribution.

Question 38

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

Question 39

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 40

Sixty percent 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 41

A manufacturer of headache medicine claims it is 70 percent 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 8 have relief within a few minutes?

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

Question 42

What is the following table called?

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

Question 43

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 44

What kind of distribution are the binomial and Poisson distributions?

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

Question 45

Which shape describes a Poisson distribution?

A)Positively skewed
B)Negatively skewed
C)Symmetrical
D)All of the above

Question 46

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 47

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 match?

A)0.5
B)⅛ or 0.125
C)⅞ or 0.875
D)Cannot be computed.

Question 48

In a Poisson distribution the mean is equal to

A)n $\pi$
B)
C)e^-x.
D)

Question 49

Which of the following is correct about a probability distribution?

A)Sum of all possible outcomes must equal 1
B)Outcomes must be mutually exclusive
C)Probability of each outcome must be between 0 and 1 inclusive
D)All of the above

Question 50

What must you know to develop a binomial probability distribution?

A)Probability of success
B)Number of trials
C)Number of successes
D)a and b only
E)a and c only

Question 51

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 52

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 53

What is the only variable in the Poisson probability formula?

A) $\pi$
B)x
C)e
D)P

Question 54

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 55

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)Probability of success remains constant from trial to trial
D)Each outcome results from two trials
E)All of the above are characteristics of the binomial distribution

Question 56

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 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 57

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 percent of the diamond wedding rings are returned.Five different customers buy five rings.What is the probability that none will be returned?

A)0.250
B)0.073
C)0.590
D)0.500
E)0.372

Question 58

The weight of an offensive linesman may be 205.15 pounds,210.23 pounds,225.05 pounds or 219.14 pounds.What is this an illustration of?

A)Continuous random variable
B)Discrete random variable
C)Complement rule
D)All of the above

Question 59

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 during some 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 60

In a large metropolitan area,past records revealed that 30 percent 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 61

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)0
C)1.6595
D)2.754

Question 62

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 63

How many experimental outcomes are possible for the binomial and the Poisson distributions? _______

Question 64

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)0.72 days
B)2.5 days
C)0.12 days
D)3 days

Question 65

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)0.875
C)0.175
D)1.0

Question 66

For the following distribution,

What is the variance of the distribution?

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

Question 67

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 for a month.
B)There is a 0.04 probability that an employee will be absent 1 day during a month.
C)There is a 0.12 probability that an employee will be absent 2 days during a month.
D)There is a 0.50 probability that an employee will be absent 0.72 days during a month.

Question 68

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 twenty-five 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 69

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)1.99
B)1.41
C)5.00
D)55.52

Question 70

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 twenty-five customers buy gasoline at this station.
What is the probability that no more than twenty pay in cash?

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

Question 71

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 twenty-five customers buy gasoline at this station.
What is the probability that at least ten pay in cash?

A)0.416
B)0.575
C)0.586
D)0.425

Question 72

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 73

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)0.420
D)0.084

Question 74

For the following distribution,

What is the mean of the distribution?

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

Question 75

For the following distribution,

What is the mean of the distribution?

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

Question 76

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 twenty-five customers buy gasoline at this station.
What is the probability that more than ten and less than fifteen customers pay in cash?

A)0.541
B)0.401
C)0.380
D)0.562

Question 77

For the following distribution,

What is the mean of the distribution?

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

Question 78

For the following distribution,

What is the variance of the distribution?

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

Question 79

For the following distribution,

What is the variance of the distribution?

A)2.1
B)0.156
C)0.395
D)1.000

Question 80

In a Poisson distribution the variance is equal to

A)n $\pi$ .
B)
C)e^-x.
D)