Deck 5: Discrete Probability Distributions

Question 1

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

Answer 1

81 days

Question 2

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 random variable of interest is continuous.

Answer 2

The random variable of interest is continuous.

Question 3

In a binomial distribution,

A) the random 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.

Answer 3

the probability of event of interest π is stable from trial to trial.

Question 4

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) all of the above
D) none of the above

Question 5

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 6

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

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) all of the above
D) none of the above

Question 8

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 9

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 10

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 average 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) all of the above
D) none of the above

Question 11

If the outcomes of a random 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 12

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 13

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 14

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) all of the above
D) none of the above

Question 15

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) all of the above
D) none of the above

Question 16

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

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

Question 17

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) all of the above
D) none of the above

Question 18

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) all of the above
D) none of the above

Question 19

A campus program evenly enrolls undergraduate and graduate students. If a random sample of four 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 four students selected are undergraduate students?

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

Question 20

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 average cost for all weekly rat purchases is $13.00.
D) The rat cost that occurs more often than any other is $13.00.

Question 21

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 22

TABLE 5-2
A certain type of new business succeeds 60% of the time. Suppose that three such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).
Referring to Table 5-2, the probability that at least one business succeeds is ________.

Question 23

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

Question 24

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

Question 25

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

Question 26

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 27

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

Question 28

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

Question 29

TABLE 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have two such alarms in your home and they operate independently.
Referring to Table 5-1, the probability that both sound an alarm in the presence of smoke is ________.

Question 30

TABLE 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have two such alarms in your home and they operate independently.
Referring to Table 5-1, the probability that neither sound an alarm in the presence of smoke is ________.

Question 31

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

Question 32

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

Question 33

TABLE 5-2
A certain type of new business succeeds 60% of the time. Suppose that three such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).
Referring to Table 5-2, the probability that exactly one business succeeds is ________.

Question 34

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

Question 35

TABLE 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have two such alarms in your home and they operate independently.
Referring to Table 5-1, the probability that at least one sounds an alarm in the presence of smoke is ________.

Question 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

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 42

TABLE 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 double satellite media.

Referring to Table 5-3, the standard deviation of the number of retransmissions is ________.

Question 43

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 44

TABLE 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 double satellite media.

Referring to Table 5-3, the probability of no retransmissions is ________.

Question 45

TABLE 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 double satellite media.

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 46

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 47

TABLE 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 double satellite media.

Referring to Table 5-3, the probability of at least one retransmission is ________.

Question 48

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

Question 49

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 50

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 51

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

Question 52

TABLE 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 double satellite media.

Referring to Table 5-3, the variance for the number of retransmissions is ________.

Question 53

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

Question 54

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 55

TABLE 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 double satellite media.

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

TABLE 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 double satellite media.

Referring to Table 5-3, the mean or expected value for the number of retransmissions is ________.

Question 57

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 58

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

Question 59

TABLE 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 double satellite media.

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 60

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 61

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 three power outages in a year is ________.

Question 62

TABLE 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 double satellite media.

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 two times is ________.

Question 63

TABLE 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon.

Referring to Table 5-4, the mean or expected value of the number of accidents is ________.

Question 64

TABLE 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 double satellite media.

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 65

TABLE 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon.

Referring to Table 5-4, the probability of three accidents is ________.

Question 66

The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 10 calls a day. The probability of seven 911 calls in a day is ________.

Question 67

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 threepower outages in a year is ________.

Question 68

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 69

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 70

TABLE 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 double satellite media.

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 71

The number of 911 calls in Butte, Montana, 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 72

TABLE 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 double satellite media.

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 73

The number of 911 calls in Butte, Montana, 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 74

TABLE 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon.

Referring to Table 5-4, the standard deviation of the number of accidents is ________.

Question 75

The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 10 calls a day. The probability of two or more 911 calls in a day is ________.

Question 76

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 77

TABLE 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon.

Referring to Table 5-4, the variance 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 of 6 outages per year. The probability that there will be at least one power outage in a year is ________.

Question 79

TABLE 5-4
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon.

Referring to Table 5-4, the probability of at least one accident is ________.

Question 80

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 one power outage in a year is ________.