Chapter 11.3, Problem 13E

(a)

To determine

To find: The probability that the customer is on hold less than 30 minutes.

Answer to Problem 13E

The probability that the customer is on hold less than 30 minutes is $95\%$ .

Explanation of Solution

Given:

The expression for the probability is $P=1-e^{-mt}$ .

Calculation:

Consider the given model is,

  $P=1-e^{-mt}$

Then,

  $\begin{array}{c}P=1-e^{-\left(-6\right)\left(0.5\right)}\\ =95\%\end{array}$

(b)

To determine

To find: The amount of the time after which 50% customer are served.

Answer to Problem 13E

The graph is shown in Figure 4 and it shows that after 0.02 hours 1.2 min the customers are served.

Explanation of Solution

Given:

The average calls are 34 calls per hour.

Calculation:

The average call is 34 then the model is,

  $P=1-e^{-34t}$

By the use graphing utility press Y= and enter the model in the calculator as shown in Figure 1

  

Figure 1

Press the window button and input the parameters as shown in Figure 2

  

Figure 2

The graph for the given model is shown in Figure 3 and is obtained by pressing the graph button.

  

Figure 3

Press the graph button trace a point on the graph as shown in Figure 4

  

Figure 4

Thus, the graph is shown in Figure 4 and it shows that after 0.02 hours 1.2 min the customers are served.