   Chapter 13.7, Problem 44E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Customer service The duration t (in minutes) of customer service calls received by a certain company is given by the probability density function f ( t ) = 0.4 e − 0.4 t   t ≥ 0 Find the probability that a call selected at random lasts(a) 4 minutes or more.(b) 10 minutes or more.

(a)

To determine

To calculate: The probability that a call selected at random lasts 4 minutes or more if the length of customer service calls received by a company is given by the probability density function f(t)=0.4e0.4t.

Explanation

Given Information:

The length of customer service calls received by a company is given by the probability density function f(t)=0.4e0.4t.

Formula used:

When f(x) is a continuous probability density function, then

Pr(axb)=abf(x)dx

According to the exponential rule of integrals,

exdx=ex+C

Calculation:

It is provided that the length of customer service calls received by a company is given by the probability density function,

f(t)=0.4e0.4t

Now, the formula for probability for continuous probability density function is,

Pr(axb)=abf(x)dx

Thus, to obtain the probability that a call selected at random lasts 4 minutes or more, substitute 4 for a, 0.4e0.4t for f(x) and for b in above formula to get,

P(x4)=40.4e0.4tdx

Now, use the formula, af(x)dx=limbabf(x)dx to rewrite the integral as,

P(x4)=limb4b0

(b)

To determine

To calculate: The probability that a call selected at random lasts 10 minutes or more if the length of customer service calls received by a company is given by the probability density function f(t)=0.4e0.4t.

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