Deck 5: Discrete Probability Distributions

Question 1

If n = 10 and π = 0.70, then the standard deviation of the binomial distribution is

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

Answer 1

B

Question 2

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 ________.

Answer 2

0.2373

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

D

Question 4

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 5

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 sample
100 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) hypergeometric distribution.
D) none of the above.

Question 6

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) hypergeometric distribution.
D) none of the above.

Question 7

Whenever π = 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 8

A probability distribution is an equation that

A) associates a particular 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 9

Whenever π = 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 10

If n = 10 and π = 0.70, then the mean of the binomial distribution is

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

Question 11

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 12

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 13

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

Question 14

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 past
20 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) hypergeometric distribution.
D) none of the above.

Question 15

In a binomial distribution

A) the variable X is continuous.
B) the probability of event of interest π 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.

Question 16

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 17

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution: $\begin{array}{lrrr}\text { Price: } & \$ 10.00 & \$ 12.50 & \$ 15.00 \\\hline \text { Probability: } & 0.35 & 0.40 & 0.25\end{array}$
How much should the lab budget for next year's rat orders be, assuming this distribution does not
Change?

A) $520
B) $637
C) $650
D) $780

Question 18

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 19

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) hypergeometric distribution.
D) none of the above.

Question 20

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 21

Suppose that past 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 22

Suppose that past 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 23

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

Question 24

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 25

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

Question 26

Suppose that past 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 27

Suppose that past 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 28

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

Question 29

Suppose that past 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 30

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 31

Suppose that past 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 32

Suppose that past 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 33

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 34

Suppose that past 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 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

If π remains constant in a binomial distribution, an increase in n will increase the
variance.

Question 37

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

Question 38

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

Question 39

Suppose that past 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 40

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 41

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 bag
Is 6.0. The manager is interested in analyzing the probability that any particular bag being
Inspected has fewer than 5.0 blue chocolate chips.

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

Question 42

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

Question 43

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

Question 44

On 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) hypergeometric distribution.
D) none of the above.

Question 45

A national trend predicts that women will account for half of all business travelers in the next 3
years. To attract these women business travelers, hotels are providing more amenities that women
particularly like. A recent survey of American hotels found that 70% offer hairdryers in the
bathrooms. Consider a random and independent sample of 20 hotels. Find the probability all of
the hotels in the sample offered hairdryers in the bathrooms.

Question 46

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

Question 47

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 48

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

Question 49

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

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

Question 50

A national trend predicts that women will account for half of all business travelers in the next 3
years. To attract these women business travelers, hotels are providing more amenities that women
particularly like. A recent survey of American hotels found that 70% offer hairdryers in the
bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that
more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms.

Question 51

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) hypergeometric distribution.
D) none of the above.

Question 52

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

Question 53

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

Question 54

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

Question 55

A national trend predicts that women will account for half of all business travelers in the next 3
years. To attract these women business travelers, hotels are providing more amenities that women
particularly like. A recent survey of American hotels found that 70% offer hairdryers in the
bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that at
least 9 of the hotels in the sample do not offer hairdryers in the bathrooms.

Question 56

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

Question 57

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 58

Current estimates suggest that 75% of the home-based computers in a foreign country have access
to on-line services. Suppose 20 people with home-based computers were randomly and
independently sampled. Find the probability that more than 9 of those sampled currently do not
have access to on-line services.

Question 59

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

Question 60

Current estimates suggest that 75% of the home-based computers in a foreign country have access
to on-line services. Suppose 20 people with home-based computers were randomly and
independently sampled. Find the probability that fewer than 10 of those sampled currently have
access to on-line services.

Question 61

SCENARIO 5-1
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 5-1, the standard deviation of the number of retransmissions is ________.

Question 62

SCENARIO 5-1
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 5-1, the variance for the number of retransmissions is ________.

Question 63

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 ____________.

Question 64

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 65

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 6.4 tickets per day. Find the probability that less than 6 tickets are written on a
randomly selected day from this population.

Question 66

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 67

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 68

The Department of Commerce in a particular 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 69

SCENARIO 5-1
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 5-1, the probability of no retransmissions is ________.

Question 70

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

Question 71

SCENARIO 5-2
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 5-2, the probability of 3 accidents is ________.

Question 72

SCENARIO 5-1
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 5-1, the probability of at least one retransmission is ________.

Question 73

The Department of Commerce in a particular 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 74

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

Question 75

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 6.4 tickets per day. Find the probability that exactly 6 tickets are written on a
randomly selected day from this population.

Question 76

SCENARIO 5-2
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 5-2, the variance of the number of accidents is ________.

Question 77

SCENARIO 5-2
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 5-2, the mean or expected value of the number of accidents is ________.

Question 78

SCENARIO 5-1
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 5-1, the mean or expected value for the number of retransmissions is
________.

Question 79

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

Question 80

SCENARIO 5-2
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 5-2, the probability of at least 1 accident is ________.