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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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License Renewal The waiting time t (in minutes) at a driver’s license renewal center is exponentially distributed with a mean of 15 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.

(c) Find the probability that the waiting time is less than 15 minutes.

(a)

To determine

To calculate: The probability density function for the random variable t, if the waiting time t at a driver’s license renewal center (in minutes) is exponentially distributed with a mean of 15 minutes.

Explanation

Given information:

The waiting time t at a driver’s license renewal center (in minutes) is exponentially distributed with a mean of 15 minutes.

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 at a driver’s license renewal center (in minutes) is exponentially distributed with a mean of 15 minutes.

(c)

To determine

To calculate: The probability that the waiting time is less than 15 minutes, if the waiting time t at a driver’s license renewal center (in minutes) is exponentially distributed with a mean of 15 minutes.

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