Deck 5: Some Important Discrete Probability Distributions

Question 1

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

Answer 1

C

Question 2

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

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

Answer 2

B

Question 3

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) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.
B) The number of tickets that is written most often is 6.5 tickets per day.
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.

Answer 3

C

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

Question 5

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

Question 6

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

Question 7

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) hypergeometric distribution
C) Poisson distribution
D) none of the above

Question 8

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

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

Question 9

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

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

Question 10

What type of probability distribution will most likely be used to analyze the number of chocolate chip parts per cookie in the following problem?

The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is
1). The manager is interested in analyzing the probability that any particular cookie being inspected has fewer than 5.0 chip parts.

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

Question 11

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) hypergeometric distribution
C) Poisson distribution
D) none of the above

Question 12

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

Question 13

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

Question 14

The portfolio expected return of two investments

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

Question 15

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

Question 16

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

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

Question 17

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

Question 18

The covariance

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

Question 19

Whenever p = 0.5, the binomial distribution will

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

Question 20

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

Question 21

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Returns }$
$\begin{array}{r|rr}\text { Probability}&\text { Neighb or hood } A &\text { Neighb or hood } B\\\hline .25 & -\$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}$


-Referring to Table 5-7, if you can invest 70% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio expected return of your investment?

Question 22

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

Question 23

In a binomial distribution

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

Question 24

Whenever p = 0.1 and n is small, the binomial distribution will be

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

Question 25

TABLE 5-5
From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed.
Referring to Table 5-5, what is the probability out of the 8 new cars it just received that, when each is tested, exactly half of the cars have defective radios?

Question 26

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\end{array}$



-Referring to Table 5-8, if your investment preference is to minimize the amount of risk that you have to take and do not care at all about the expected profit, will you choose a production mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the remaining for Design B?

Question 27

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 28

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:
$$\begin{array} { l | r r r } \text { Price: } & \$ 10.00 & \$ 12.50 & \$ 15.00 \\\hline \text { Probability: } & 0.35 & 0.40 & 0.25\end{array}$$
How much should the lab budget for next year's rat orders be, assuming this distribution does not change?

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

Question 29

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c |c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$


-Referring to Table 5-7, what is the variance of the gain in value for the house in neighborhood B?

Question 30

$$\text { TABLE 5-1 }$$ 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 31

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\end{array}$

-Referring to Table 5-8 if you decide to choose Design A for 70% of the production lines and Design B for the remaining production lines, what is the risk of your investment?

Question 32

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) 1.00
B) 0.16
C) 0.0625
D) 0.0256

Question 33

A probability distribution is an equation that

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

Question 34

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c| c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$

-Referring to Table 5-7, if you can invest 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio expected return of your investment?

Question 35

$\text { TABLE 5-6 }$
The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0.

-Referring to Table 5-6, what is the probability that any particular cookie being inspected has at least 6.0 chip parts.

Question 36

$\text { TABLE 5-8 }$
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\end{array}$


-Referring to Table 5-8, if you decide to choose Design A for half of the production lines and Design B for the other half, what is the risk of your investment?

Question 37

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 38

$\text { TABLE 5-8 }$
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\end{array}$


-Referring to Table 5-8, if your investment preference is to maximize your expected profit and not worry at all about the risk that you have to take, will you choose a production mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the remaining for Design B?

Question 39

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 40

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c| c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$

-Referring to Table 5-7, if you can invest 30% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

Question 41

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 42

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\\\hline\end{array}$

-Referring to Table 5-8, what is the total standard deviation of the profit if you increase the shift of your production lines and choose to produce both designs?

Question 43

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 44

Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

Referring to Table 5-8, if you decide to choose Design A for 90% of the production lines and Design B for the remaining production lines, what is the coefficient of variation of your investment?

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.
$$\begin{array} { c | c c c c } X & 0 & 1 & 2 & 3 \\\hline P ( X ) & 0.35 & 0.35 & 0.25 & 0.05\end{array}$$

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

Question 46

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 47

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c| c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$


-Referring to Table 5-7, if you can invest 30% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio expected return of your investment?

Question 48

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

Question 49

TABLE 5-6
The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0.

-Referring to Table 5-6, what is the probability that any particular cookie being inspected has fewer than 5.0 chip parts.

Question 50

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

Referring to Table 5-8, what is the variance of your profit when Design A is chosen?

Question 51

Referring to Table 5-8, what is your expected profit when Design A is chosen?

Question 52

$\text { TABLE 5-7 }$ There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c| c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$


-Referring to Table 5-7, if you can invest 10% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

Question 53

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
$$\begin{array} { l l c c } \hline \text { Probability } & \text { Taste } & \text { Design } A & \text { Design B } \\\hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310 \\0.3 & \text { more liberal } & 350 & 270\end{array}$$

-Referring to Table 5-8, what is the variance of your profit when Design B is chosen?

Question 54

$\text { TABLE 5-7 }$ There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c |c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$


-Referring to Table 5-7, what is the standard deviation of the value gain for the house in neighborhood A?

Question 55

The number of 911 calls in Butte, Montana, 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 56

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. What is the probability that at least 1 of the members chosen for the team have some prior competition experience?

Question 57

TABLE 5-5
From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed.
Referring to Table 5-5, what is the probability out of the 8 new cars it just received that, when each is tested, no more than half of the cars have non-defective radios?

Question 58

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

Question 59

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\end{array}$


-Referring to Table 5-8, if you decide to choose Design A for half of the production lines and Design B for the other half, what is the coefficient of variation of your investment?

Question 60

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:

Referring to Table 5-7, if your investment preference is to maximize your expected return while exposing yourself to the minimal amount of risk, will you choose a portfolio that will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?

Question 61

$\text { TABLE 5-2 }$ 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 62

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 63

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 64

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:

Referring to Table 5-7, what is the covariance of the two houses?

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.
$$\begin{array} { c | c c c c c c } \mathrm { X } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline P ( \mathrm { X } ) & 0.10 & 0.20 & 0.45 & 0.15 & 0.05 & 0.05\end{array}$$

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

Question 66

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 67

$\text { TABLE 5-5 }$ From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed.

-Referring to Table 5-5, what is the probability out of the 8 new cars it just received that, when each is tested, none of the cars have defective radios?

Question 68

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\end{array}$



-Referring to Table 5-8, if your investment preference is to maximize your expected profit while exposing yourself to the minimal amount of risk, will you choose a production mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the remaining for Design B?

Question 69

$\text { TABLE 5-7 }$ There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$



-Referring to Table 5-7, if your investment preference is to maximize your expected return and not worry at all about the risk that you have to take, will you choose a portfolio that will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?

Question 70

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:

Referring to Table 5-7, what is the total standard deviation of value gain if you invest in both houses?

Question 71

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\end{array}$



-Referring to Table 5-8, if you decide to choose Design A for 30% of the production lines and Design B for the remaining production lines, what is the coefficient of variation of your investment?

Question 72

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c| c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$


-Referring to Table 5-7, if you can invest 10% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio expected return of your investment?

Question 73

TABLE 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

Referring to Table 5-8, what is your expected profit when Design B is chosen?

Question 74

$$\text { TABLE 5-4 }$$ The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon.
$$\begin{array} { c | c c c c c c } \mathrm { X } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline P ( \mathrm { X } ) & 0.10 & 0.20 & 0.45 & 0.15 & 0.05 & 0.05\end{array}$$

-Referring to Table 5-4, the probability of 3 accidents is ____.

Question 75

$$\text { TABLE 5-8 }$$ Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
$\begin{array}{llcc}\hline \text { Probability}& \text {Taste }&\text { Design A } & \text { Design B }\\ \hline 0.2 & \text { more conservative } & 180 & 520 \\0.5 & \text { no change } & 230 & 310\\0.3&\text { more liberal }&350&270\end{array}$



-Referring to Table 5-8, what is the expected profit if you increase the shift of your production lines and choose to produce both designs?

Question 76

$\text { TABLE 5-7 }$ There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$



-Referring to Table 5-7, what is the expected value gain for the house in neighborhood B?

Question 77

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 78

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 79

TABLE 5-7
There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Returns }$
$\begin{array}{l}\begin{array} { c |c c } \text { Probability}& \text { Neighb or hood A}& \text { Neighb or hood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\.40 & \$ 10,000 & \$ 25,000 \\.35 & \$ 40,500 & \$ 10,500\end{array}\end{array}$


-Referring to Table 5-7, if you can invest 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

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 probability that she gets audited at least once is ____.