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The lifetime of a cooling fan, in hours, that is used in a

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 11E Chapter 4.8

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 11E

The lifetime of a cooling fan, in hours, that is used in a computer system has the Weibull distribution with α = 1.5 and β = 0.0001.

a. What is the probability that a fan lasts more than 10,000 hours?

b. What is the probability that a fan lasts less than 5000 hours?

c. What is the probability that a fan lasts between 3000 and 9000 hours?

Step-by-Step Solution:

Step 1 of 3:

The lifetime of a cooling fan that is used in a computer has weibull distribution with  .

We have to find

The Probability that fan last more than 10,000 hours.The Probability that fan last less than 5000 hours. The Probability that fan last between 3000 and 9000 hours.

Step 2 of 3:

Let T be the lifetime of the fan which follows weibull distribution with parameters and .

So the pdf of T is

                           f(t) = , .

                                 = (1.5) (0.0001

And the density function of T is

                          F(t) = P(

                               =  1-

 

                               =   1-

              F(t) =  1-

Probability that fan last more than 10,000 hours.

 

        P(T>10,000) = 1- P(

                             =  1- F(10,000)

                             =  1- (1- )

 

                           =  

                           =    0.3679

   P(T>10,000)   =     0.3679

Therefore the probability that fan last more than 10,000 hours is 0.3679.

Step 3 of 3

Chapter 4.8, Problem 11E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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