Deck 5: Discrete Probability Distributions

Question 1

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.

Answer 1

the amount you expect to "gain" in the long run over many plays.

Question 2

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.

Answer 2

Binomial distribution

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

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 5

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 6

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.

Question 7

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 8

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 9

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 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

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

What type of probability distribution will most likely be used to analyze the number of cars with defective radios in the following problem? From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. The sales manager of one dealership wants to predict the probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios.

A) Binomial distribution
B) Poisson distribution
C) Hypergeometric distribution
D) None of the above.

Question 13

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 14

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 15

A stock analyst was provided with a list of 25 stocks. He was expected to pick 3 stocks from the list whose prices are expected to rise by more than 20% after 30 days. In reality, the prices of only 5 stocks would rise by more than 20% after 30 days. If he randomly selected 3 stocks from the list, he would use what type of probability distribution to compute the probability that all of the chosen stocks would appreciate more than 20% after 30 days?

A) Binomial distribution
B) Poisson distribution
C) Hypergeometric distribution
D) None of the above.

Question 16

The covariance

A) must be between -1 and +1.
B) must be positive.
C) can be positive or negative.
D) must be less than +1.

Question 17

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 18

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) Hypergeometric distribution
D) None of the above.

Question 19

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 20

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 21

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 22

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 23

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

Question 24

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

Question 25

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 26

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

Question 27

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

Question 28

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

Question 29

The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution.

Question 30

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

Question 31

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 32

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 33

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

Question 34

A financial analyst is presented with information on the past records of 60 start-up companies and told that in fact only 3 of them have managed to become highly successful. He selected 3 companies from this group as the candidates for success. To analyze his ability to spot the companies that will eventually become highly successful, he will use what type of probability distribution?

A) Binomial distribution
B) Poisson distribution
C) Hypergeometric distribution
D) None of the above.

Question 35

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

Question 36

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

Question 37

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 38

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

Question 39

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 40

The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution.

Question 41

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 2 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 42

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

Question 43

TABLE 5-2
A certain type of new business succeeds 60% of the time. Suppose that 3 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 3 businesses fail is ________.

Question 44

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 2 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 45

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 2 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 46

The variance of the sum of two investments will be equal to the sum of the variances of the two investments plus twice the covariance between the investments.

Question 47

TABLE 5-2
A certain type of new business succeeds 60% of the time. Suppose that 3 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 3 businesses succeed is ________.

Question 48

If the covariance between two investments is zero, the variance of the sum of the two investments will be equal to the sum of the variances of the investments.

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 exactly 4 prefer Brand C is ________.

Question 50

The covariance between two investments is equal to the sum of the variances of the investments.

Question 51

The variance of the sum of two investments will be equal to the sum of the variances of the two investments when the covariance between the investments is zero.

Question 52

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 53

TABLE 5-2
A certain type of new business succeeds 60% of the time. Suppose that 3 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 1 business succeeds is ________.

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 at least 1 prefers Brand C is ________.

Question 55

The expected return of a two-asset portfolio is equal to the product of the weight assigned to the first asset and the expected return of the first asset plus the product of the weight assigned to the second asset and the expected return of the second asset.

Question 56

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

Question 57

TABLE 5-2
A certain type of new business succeeds 60% of the time. Suppose that 3 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 1 business succeeds is ________.

Question 58

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

Question 59

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 60

The expected return of the sum of two investments will be equal to the sum of the expected returns of the two investments plus twice the covariance between the investments.

Question 61

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 62

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 63

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 64

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 1 accident is ________.

Question 65

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 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

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 68

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 69

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 70

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 3 accidents is ________.

Question 71

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 72

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 73

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 74

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 75

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 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 probability that she gets audited at least once is ________.

Question 77

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 78

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 79

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 80

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 ________.