Chapter 8, Problem 23RE

### Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636

Chapter
Section

### Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636
Textbook Problem

# The length of time spent waiting in line at a certain bank is modeled by an exponential density function with mean 8 minutes. (a) What is the probability that a customer is served in the first 3 minutes? (b) What is the probability that a customer has to wait more than 10 minutes? (c) What is the median waiting time?

(a)

To determine

To find:

The probability that a customer is served in the first 3 minutes.

Explanation

Given information:

The length of time spent for waiting in line is modeled by an exponential density function

The mean value is Î¼=8â€‰minutes .

Calculation:

The general expression for the exponential density function is f(t)={0â€‰ifâ€‰t<01Î¼eâˆ’tÎ¼â€‰ifâ€‰tâ‰¥0 .

Here, the mean is Î¼ .

Rearrange the exponential density function with mean Î¼=8â€‰min as follows:

f(t)={0â€‰ifâ€‰t<018eâˆ’t8â€‰ifâ€‰tâ‰¥0

Show the function as follows:

f(t

(b)

To determine

To find:

The probability that customer has to wait more than 10 minutes.

(c)

To determine

To find:

The median waiting time.

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