Deck 5: Discrete Probability Distributions

Question 1

In a binomial distribution

A)the variable X is continuous.
B)the probability of event of interest $\pi$ is stable from trial to trial.
C)the number of trials n must be at least 30.
D)the results of one trial are dependent on the results of the other trials.

Answer 1

the probability of event of interest $\pi$ is stable from trial to trial.

Question 2

What type of probability distribution will most likely be used to analyze warranty repair needs on new cars in the following problem?The service manager for a new automobile dealership reviewed dealership records of the past20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days.Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05.The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.

A)binomial distribution.
B)Poisson distribution.
C)Either of the above
D)none of the above.

Answer 2

binomial distribution.

Question 3

Which of the following about the binomial distribution is not a true statement?

A)The probability of the event of interest must be constant from trial to trial.
B)Each outcome is independent of the other.
C)Each outcome may be classified as either "event of interest" or "not event of interest."
D)The variable of interest is continuous.

Answer 3

The variable of interest is continuous.

Question 4

The portfolio expected return of two investments

A)will be higher when the covariance is zero.
B)will be higher when the covariance is negative.
C)will be higher when the covariance is positive.
D)does not depend on the covariance.

Question 5

Whenever $\pi$ = 0.5, the binomial distribution will

A)always be symmetric.
B)be symmetric only if n is large.
C)be right-skewed.
D)be left-skewed.

Question 6

A probability distribution is an equation that

A)associates a probability of occurrence with each outcome.
B)measures outcomes and assigns values of X to the simple events.
C)assigns a value to the variability of the set of events.
D)assigns a value to the center of the set of events.

Question 7

A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.025.To find the probability that exactly 20 of the computers will require repair on a given day, one will use what type of probability distribution?

A)binomial distribution.
B)Poisson distribution.
C)Either of the above
D)none of the above.

Question 8

If the outcomes of a variable follow a Poisson distribution, then them

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

Question 9

n the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store.What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter?

A)binomial distribution.
B)Poisson distribution.
C)Either of the above
D)none of the above.

Question 10

Whenever $\pi = 0.1$ and n is small, the binomial distribution will be

A)symmetric.
B)right-skewed.
C)left-skewed.
D)None of the above.

Question 11

If n = 10 and $\pi = 0.70$ , then the mean of the binomial distribution is

A)0.07
B)1.45.
C)7.00
D)14.29

Question 12

A professor receives, on average, 24.7 e-mails from students the day before the midterm exam.To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?

A)binomial distribution.
B)Poisson distribution.
C)Either of the above
D)none of the above.

Question 13

The connotation "expected value" or "expected gain" from playing roulette at a casino means

A)the amount you expect to "gain" on a single play.
B)the amount you expect to "gain" in the long run over many plays.
C)the amount you need to "break even" over many plays.
D)the amount you should expect to gain if you are lucky.

Question 14

A campus program evenly enrolls undergraduate and graduate students.If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?

A)0.0256
B)0.0625
C)0.16
D)1.00

Question 15

What type of probability distribution will most likely be used to analyze the number of blue chocolate chips per bag in the following problem?The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.When the production process is in control, the mean number of blue chocolate chips per bagis 6.0.The manager is interested in analyzing the probability that any bag being inspected has fewer than 5.0 blue chocolate chips.

A)binomial distribution.
B)Poisson distribution.
C)Either of the above
D)none of the above.

Question 16

A multiple-choice test has 30 questions.There are 4 choices for each question.A student who has not studied for the test decides to answer all questions randomly.What type of probability distribution can be used to figure out his chance of getting at least 20 questions right?

A)binomial distribution.
B)Poisson distribution.
C)Either of the above
D)none of the above.

Question 17

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio- Pulmonary Resuscitation (CPR).In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

A)5 days
B)45 days
C)65 days
D)81 days

Question 18

What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem?An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims.It is known that the industry proportion for false claims is 3%.The consulting firm has decided to randomly and independently sample100 of the company's insurance claims.They believe the number of these 100 that are false will yield the information the company desires.

A)binomial distribution.
B)Poisson distribution.
C)Either of the above
D)none of the above.

Question 19

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week.Interpret this value.

A)Most of the weeks resulted in rat costs of $13.00.
B)The median cost for the distribution of rat costs is $13.00.
C)The expected or mean cost for all weekly rat purchases is $13.00.
D)The rat cost that occurs more often than any other is $13.00.

Question 20

If n = 10 and $\pi = 0.70$ , then the standard deviation of the binomial distribution is

A)0.07
B)1.45
C)7.00
D)14.29

Question 21

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process.The mean number of airplanes arriving per minute is 3.The probability that exactly 6 planes arrive in the next minute is 0.05041.

Question 22

The diameters of 10 randomly selected bolts have a binomial distribution.

Question 23

SCENARIO 5-2
A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete, so it is reasonable to believe that their relative successes would be independent).
Referring to Scenario 5-2, the probability that at least 1 business succeeds is .

Question 24

In a Poisson distribution, the mean and standard deviation are equal.

Question 25

The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day.Interpret the value of the mean.

A)The number of tickets that is written most often is 6.5 tickets per day.
B)Half of the days have less than 6.5 tickets written, and half of the days have more than 6.5 tickets written.
C)If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.
D)The mean has no interpretation since 0.5 ticket can never be written.

Question 26

If $\pi$ remains constant in a binomial distribution, an increase in n will increase the variance.

Question 27

If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = .

Question 28

SCENARIO 5-2
A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete, so it is reasonable to believe that their relative successes would be independent).
Referring to Scenario 5-2, the probability that exactly 1 business succeeds is .

Question 29

In a Poisson distribution, the mean and variance are equal.

Question 30

The number of customers arriving at a department store in a 5-minute period has aPoisson distribution.

Question 31

SCENARIO 5-1
The probability that a smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently.
Referring to Scenario 5-1, the probability that at least one sounds an alarm in the presence of smoke is _.

Question 32

If $\pi$ remains constant in a binomial distribution, an increase in n will not change the mean.

Question 33

SCENARIO 5-2
A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete, so it is reasonable to believe that their relative successes would be independent).
Referring to Scenario 5-2, the probability that all 3 businesses succeed is .

Question 34

Another name for the mean of a probability distribution is its expected value.

Question 35

Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% of the time.In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

Question 36

The largest value that a Poisson random variable X can have is n.

Question 37

SCENARIO 5-1
The probability that a smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently.
Referring to Scenario 5-1, the probability that neither sound an alarm in the presence of smoke is_.

Question 38

SCENARIO 5-1
The probability that a smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently.
Referring to Scenario 5-1, the probability that both sound an alarm in the presence of smoke is_.

Question 39

The Poisson distribution can be used to model a continuous random variable.

Question 40

SCENARIO 5-2
A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete, so it is reasonable to believe that their relative successes would be independent).
Referring to Scenario 5-2, the probability that all 3 businesses fail is _.

Question 41

SCENARIO 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network.
Referring to Scenario 5-3, the probability of at least one retransmission is .

Question 42

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that exactly 1 prefers brand C is .

Question 43

SCENARIO 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network.
Referring to Scenario 5-3, the standard deviation of the number of retransmissions is _.

Question 44

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that exactly 4 prefer brand C is .

Question 45

SCENARIO 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network.
Referring to Scenario 5-3, the variance for the number of retransmissions is _.

Question 46

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that exactly 3 prefer brand C is .

Question 47

SCENARIO 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network.
Referring to Scenario 5-3, the probability of no retransmissions is .

Question 48

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that more than 3 prefer brand C is .

Question 49

In a game called Taxation and Evasion, a player rolls a pair of dice.If on any turn the sum is 7,11, or 12, the player gets audited.Otherwise, she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The probability that she gets audited once is .

Question 50

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The mean number that you would expect to prefer brand C is_.

Question 51

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that 2 or fewer prefer brand C is .

Question 52

If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = .

Question 53

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The variance of the number that prefer brand C is .

Question 54

If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = .

Question 55

SCENARIO 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network.
In a game called Taxation and Evasion, a player rolls a pair of dice.If, on any turn, the sum is 7,11, or 12, the player gets audited.Otherwise, she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The probability that she does not get audited is .

Question 56

In a game called Taxation and Evasion, a player rolls a pair of dice.If on any turn the sum is 7,11, or 12, the player gets audited.Otherwise, she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The probability that she gets audited no more than 2 times is .

Question 57

In a game called Taxation and Evasion, a player rolls a pair of dice.If on any turn the sum is 7,11, or 12, the player gets audited.Otherwise, she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The probability that she gets audited at least once is _.

Question 58

SCENARIO 5-3
The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network.
Referring to Scenario 5-3, the mean or expected value for the number of retransmissions is_.

Question 59

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that fewer than 2 prefer brand C is .

Question 60

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that at least 1 prefers brand C is .

Question 61

SCENARIO 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest.
Referring to Scenario 5-4, the probability of 3 accidents is .

Question 62

The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.The probability of seven or eight 911 calls in a day is .

Question 63

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of6 outages per year.The probability that there will be at least 1 power outage in a year is.

Question 64

SCENARIO 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest.
Referring to Scenario 5-4, the probability of at least 1 accident is .

Question 65

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of6 outages per year.The probability that there will be exactly 3 power outages in a year is.

Question 66

In a game called Taxation and Evasion, a player rolls a pair of dice.If on any turn the sum is 7,11, or 12, the player gets audited.Otherwise, she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The expected number of times she will be audited is _.

Question 67

SCENARIO 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest.
Referring to Scenario 5-4, the standard deviation of the number of accidents is .

Question 68

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of6 outages per year.The probability that there will be at least 3 power outages in a year is.

Question 69

The number of 911 calls in a small city has a Poisson distribution with a mean of 10.0 calls a day.The standard deviation of the number of 911 calls in a day is .

Question 70

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of6 outages per year.The variance of the number of power outages is .

Question 71

The Department of Commerce in a state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.Find the probability that exactly 5 bankruptcies occur next month.

Question 72

SCENARIO 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest.
Referring to Scenario 5-4, the variance of the number of accidents is _.

Question 73

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of6 outages per year.The probability that there will be no more than 1 power outage in a year is.

Question 74

In a game called Taxation and Evasion, a player rolls a pair of dice.If on any turn the sum is 7,11, or 12, the player gets audited.Otherwise, she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The standard deviation of the number of times she will be audited is .

Question 75

The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.The probability of seven 911 calls in a day is .

Question 76

In a game called Taxation and Evasion, a player rolls a pair of dice.If on any turn the sum is 7,11, or 12, the player gets audited.Otherwise, she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The variance of the number of times she will be audited is _.

Question 77

SCENARIO 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest.
Referring to Scenario 5-4, the mean or expected value of the number of accidents is .

Question 78

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of6 outages per year.The probability that there will be between 1 and 3 inclusive power outages in a year is _.

Question 79

The Department of Commerce in a state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.Find the probability that more than 3 bankruptcies occur next month.

Question 80

The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.The probability of 2 or more 911 calls in a day is .