Question 1

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:
$$\begin{array} { | c | c | c | } 
\hline &  { \text { Returns } } \
\hline \text { Probability } & \text { Neighborhood A } & \text { Neighborhood B } \
\hline .25 & - \$ 22,500 & \$ 30,500 \
\hline .40 & \$ 10,000 & \$ 25,000 \
\hline .35 & \$ 40,500 & \$ 10,500 \
\hline
\end{array}$$
-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?

Accepted Answer

The answer of TABLE 5-7
There are two houses with almost...

Question 2

Whenever π = 0.5, the binomial distribution will

Accepted Answer

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

Question 3

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

Accepted Answer

The answer of If X has a binomial distribution with...

Question 4

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?

Accepted Answer

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

Question 5

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 ________.

Accepted Answer

The answer of TABLE 5-1
The probability that a particular type...

Question 6

TABLE 5-9
A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution.
-Referring to Table 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have less than two or more than eight mishandled bags?

Accepted Answer

The answer of TABLE 5-9
A major hotel chain keeps a...

Question 7

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.
 $$\begin{array} { | c | c | c | c | c | } 
\hline X & 0 & 1 & 2 & 3 \
\hline P ( X ) & 0.35 & 0.35 & 0.25 & 0.05 \
\hline
\end{array}$$
-Referring to Table 5-3, the variance for the number of retransmissions is ________.

Accepted Answer

The answer of TABLE 5-3
The following table contains the probability...

Question 8

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.
 $$\begin{array} { | c | c | c | c | c | } 
\hline X & 0 & 1 & 2 & 3 \
\hline P ( X ) & 0.35 & 0.35 & 0.25 & 0.05 \
\hline
\end{array}$$
-Referring to Table 5-3, the probability of no retransmissions is ________.

Accepted Answer

The answer of TABLE 5-3
The following table contains the probability...

Question 9

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.

Accepted Answer

A) True 
 B)False

Question 10

TABLE 5-9
A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution.
-Referring to Table 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have between two and four inclusive mishandled bags?

Accepted Answer

The answer of TABLE 5-9
A major hotel chain keeps a...

Question 11

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.
 $$\begin{array} { | c | c | c | c | c | } 
\hline X & 0 & 1 & 2 & 3 \
\hline P ( X ) & 0.35 & 0.35 & 0.25 & 0.05 \
\hline
\end{array}$$
-Referring to Table 5-3, the mean or expected value for the number of retransmissions is ________.

Accepted Answer

The answer of TABLE 5-3
The following table contains the probability...

Question 12

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.
 $$\begin{array} { | c | c | c | c | } 
\hline \text { Probability } & \text { Taste } & \text { Design A } & \text { Design B } \
\hline 0.2 & \text { more conservative } & 180 & 520 \
\hline 0.5 & \text { no change } & 230 & 310 \
\hline 0.3 & \text { more liberal } & 350 & 270 \
\hline
\end{array}$$
-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 coefficient of variation of your investment?

Accepted Answer

The answer of TABLE 5-8
Two different designs on a new...

Question 13

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 ________.

Accepted Answer

The answer of The number of power outages at a...

Question 14

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 exactly half of the members chosen for the team have some prior competition experience?

Accepted Answer

The answer of A debate team of 4 members for...

Question 15

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.

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

The answer of TABLE 5-4
The following table contains the probability...

Question 17

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 ________.

Accepted Answer

The answer of In a game called Taxation and Evasion,...

Question 18

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:
$$\begin{array} { | c | c | c | } 
\hline &  { \text { Returns } } \
\hline \text { Probability } & \text { Neighborhood A } & \text { Neighborhood B } \
\hline .25 & - \$ 22,500 & \$ 30,500 \
\hline .40 & \$ 10,000 & \$ 25,000 \
\hline .35 & \$ 40,500 & \$ 10,500 \
\hline
\end{array}$$
-Referring to Table 5-7, what is the standard deviation of the value gain for the house in neighborhood B?

Accepted Answer

The answer of TABLE 5-7
There are two houses with almost...

Question 19

From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. Which of the following distributions would you use to determine the probability that out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios?

Accepted Answer

A)  Hypergeometric distribution 
B)  Poisson distribution 
C)  Uniform distribution 
D)  Binomial distribution

Question 20

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?

Accepted Answer

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

Exam 5: Discrete Probability Distributions

Whenever π = 0.5, the binomial distribution will

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

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?

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.

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 ________.

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.

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 ________.