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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Waiting Time The waiting time t (in minutes) for service in a store is exponentially distributed with a mean of 5 minutes.

(a) Find the probability density function for the random variable t.

(b) Find the probability that the waiting time is within one standard deviation of the mean.

(a)

To determine

To calculate: The probability density function for the random variable t, if the waiting time t (in minutes) is exponentially distributed with a mean of 5 minutes for service in a store.

Explanation

Given information:

The waiting time t (in minutes) is exponentially distributed with a mean of 5 minutes for service in a store.

Formula used:

The exponential probability density function,

f(x)=aeax  , 0x<

Here, an expected value is,

μ=1a

Calculation:

The provided time is t,

Consider a function as f with respect to t,

Use the formula of the exponential probability density function, the function will be,

f(t)=aeat

To find the value of a use the formula μ

(b)

To determine

To calculate: The probability that the waiting time is within one standard deviation of the mean, if the waiting time t (in minutes) is exponentially distributed with a mean of 5 minutes for service in a store.

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