Chapter 6, Problem 39SE

a.

To determine

Find the mean monthly revenue for the minibar service at this hotel.

Answer to Problem 39SE

The mean monthly revenue for the minibar service at this hotel is $10,120.

Explanation of Solution

Calculation:

It is given that the monthly revenues from the minibar service are normally distributed with a standard deviation of $2,200. The mean annual revenue per hotel room is $368.

Assume that x denotes the monthly revenue for the minibar service at the hotel.

The mean monthly revenue for the minibar service at this hotel is obtained as follows:

$\begin{array}{c}\text{Mean monthly revenue }=\frac{\left(368\times 330\right)}{12}\\ =10,120\end{array}$

Thus, the mean monthly revenue for the minibar service at this hotel is $10,120.

b.

To determine

Obtain the probability that the minibar service provides over $12,000 in monthly revenues for this hotel.

Answer to Problem 39SE

The probability that the minibar service provides over $12,000 in monthly revenues for this hotel is 0.1977.

Explanation of Solution

Calculation:

The probability that the minibar service provides over $12,000 in monthly revenues for this hotel can be written as $P\left(x>12,000\right)$.

Now,

$P\left(x>12,000\right)=1-P\left(x\le 12,000\right)$

Probability value:

Software procedure:

Step-by-step procedure to obtain probability value using the EXCEL:

• Open an EXCEL sheet and select the cell A1.
• Enter the formula =1-NORM.DIST(12,000,10,120,2200,TRUE) in the cell A1.
• Press Enter.

Output obtained using the EXCEL software is given below:

Hence, $P\left(x>12,000\right)=0.1964$.

Thus, the probability that the minibar service provides over $12,000 in monthly revenues for this hotel is 0.1964.

c.

To determine

Find the probability that the minibar service provides less than $7,500 in monthly revenues for this hotel.

Answer to Problem 39SE

The probability that the minibar service provides less than $7,500 in monthly revenues for this hotel is 0.1168.

Explanation of Solution

Calculation:

The probability that the minibar service provides less than $7,500 in monthly revenues for this hotel can be written as $P\left(x<7,500\right)$.

Probability value:

Software procedure:

Step-by-step procedure to obtain the probability value using the EXCEL:

• Open an EXCEL sheet and select the cell A1.
• Enter the formula =NORM.DIST(7,500,10,120,22,00,TRUE) in the cell A1.
• Press Enter.

Output obtained using the EXCEL software is given below:

Hence, $P\left(x<7,500\right)=0.1168$.

Thus, the probability that the minibar service provides less than $7,500 in monthly revenues for this hotel is 0.1168.

d.

To determine

Find the increase in the annual revenues for the upgraded minibar service.

Check whether one would agree with the strategy of upgrading the hotel’s minibar selections.

Answer to Problem 39SE

The increase in the annual revenues for the upgraded minibar service is $17,160.

Explanation of Solution

Calculation:

It is given that the new minibar offerings are expected to raise the mean annual revenue to $420 per room. The monthly revenues from the minibar service are normally distributed with a standard deviation of $2,500.

Then, the mean monthly revenue for the minibar service at this hotel is obtained as follows:

$\begin{array}{c}\text{Mean monthly revenue }=\frac{\left(420\times 330\right)}{12}\\ =11,550\end{array}$

Thus, the mean monthly revenue for the minibar service at this hotel is $11,550.

The probability that the minibar service provides over $12,000 in monthly revenues for this hotel can be written as $P\left(x>12,000\right)=1-P\left(x\le 12,000\right)$.

Probability value:

Software procedure:

Step-by-step procedure to obtain the probability value using the EXCEL:

• Open an EXCEL sheet and select the cell A1.
• Enter the formula =1-NORM.DIST(12,000,11,550,2500,TRUE) in the cell A1.
• Press Enter.

Output obtained using the EXCEL software is given below:

Hence, $P\left(x>12,000\right)=0.4286$.

Thus, the probability that the minibar service provides over $12,000 in monthly revenues for this hotel is 0.4286.

The probability that the minibar service provides less than $7,500 in monthly revenues for this hotel can be written as $P\left(x<7,500\right)$.

Probability value:

Software procedure:

Step-by-step procedure to obtain the probability value using the EXCEL:

• Open an EXCEL sheet and select the cell A1.
• Enter the formula =NORM.DIST(7,500,10,120,25,00,TRUE) in the cell A1.
• Press Enter.

Output obtained using the EXCEL software is given below:

Hence, $P\left(x<7,500\right)=0.0526$.

Thus, the probability that the minibar service provides less than $7,500 in monthly revenues for this hotel is 0.0526.

$\begin{array}{c}\text{Current annul revenue}=\left(\$368\right)\left(330\right)\\ =\$121,440\end{array}$

$\begin{array}{c}\text{New annul revenue}=\left(\$420\right)\left(330\right)\\ =\$138,600\end{array}$

An increase in annual revenue is obtained as follows:

$\begin{array}{c}\text{Increase in annual revenue }=138,600-121,440\\ =17,160\end{array}$

Thus, the higher probability of monthly revenues over $12,000 makes the upgraded minibar service worthwhile.