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:
  $\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?

Accepted Answer

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

Question 2

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

Accepted Answer

The probability that a teacher is certified in CPR is 36/80. Multiply this probability by 180 days to find the expected number of days a certified teacher is on bus duty: (36/80) * 180 = 81 days.

Question 3

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.

Accepted Answer

In a binomial distribution, the probability of the event of interest remains stable from trial to trial. This is one of the defining characteristics of a binomial distribution. The number of trials does not necessarily have to be at least 30, and the results of one trial are independent of the results of other trials. Additionally, the random variable X in a binomial distribution is discrete, not continuous.

Question 4

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

Accepted Answer

When p = 0.1 and n is small, the binomial distribution is right-skewed because the probability of success is low, leading to a distribution with a long tail on the right.

Question 5

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?

Accepted Answer

The answer of TABLE 5-5
From an inventory of 48 new...

Question 6

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?

Accepted Answer

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

Question 7

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 ______.

Accepted Answer

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

Question 8

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

Accepted Answer

The expected price for 100 rats is calculated as: (0.35 * $10.00) + (0.40 * $12.50) + (0.25 * $15.00) = $12.25. For 52 weeks, the budget is 52 * $12.25 = $637.

Question 9

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?

Accepted Answer

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

Question 10

$$\text { TABLE 5-1 }$$ 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 _______.

Accepted Answer

The answer of $$\text { TABLE 5-1 }$$ The probability...

Question 11

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?

Accepted Answer

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

Question 12

A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?
A) 1.00
B) 0.16
C) 0.0625
D) 0.0256

Accepted Answer

There are only 2 types of students: undergraduate and graduate, each with 50% probability of being selected. Since the selection is without replacement, the probability of selecting an undergraduate student decreases with each selection. The probability that the first student selected is an undergraduate is 0.5. The probability that the second student selected is an undergraduate given that the first was an undergraduate is 0.4 (since there are now more graduate students left in the program). Similarly, the probability that the third student selected is an undergraduate given that the first 2 were undergraduate is 0.33 and the probability that the fourth student selected is an undergraduate given that the first 3 were undergraduate is 0.25. Therefore, the probability that all 4 randomly selected students are undergraduate is: 
0.5 x 0.4 x 0.33 x 0.25 = 0.0625 (or 6.25%)

Question 13

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.

Accepted Answer

A probability distribution associates a particular probability of occurrence with each outcome in the sample space. It does not assign a value to the center, measure outcomes and assign values, or assign a value to the variability in the sample space.

Question 14

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?

Accepted Answer

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

Question 15

$\text { TABLE 5-6 }$
 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.

Accepted Answer

The answer of $\text { TABLE 5-6 }$
 The quality...

Question 16

$\text { TABLE 5-8 }$
 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?

Accepted Answer

The answer of $\text { TABLE 5-8 }$
 Two different...

Question 17

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.

Accepted Answer

The answer of A national trend predicts that women will...

Question 18

$\text { TABLE 5-8 }$
 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?

Accepted Answer

The answer of $\text { TABLE 5-8 }$
 Two different...

Question 19

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.

Accepted Answer

The answer of A national trend predicts that women will...

Question 20

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?

Accepted Answer

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

Quiz 5: Some Important Discrete Probability Distributions

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?

In a binomial distribution

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

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 ______.

A probability distribution is an equation that