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# The lifetime of a bearing (in years) follows the Weibull

ISBN: 9780073401331 38

## Solution for problem 17SE Chapter 4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 17SE

The lifetime of a bearing (in years) follows the Weibull distribution with parameters α = 1.5 and β = 0.8.

a. What is the probability that a bearing lasts more than 1 year?

b. What is the probability that a bearing lasts less than 2 years?

Step-by-Step Solution:

Step 1 of 3:

It is given that lifetime of a bearing( in years) follows weibull distribution with =1.5 and

=0.8.

Let us denote the lifetime of the bearing as X. Then X~Weibull(=1.5,=0.8).

The probability mass function of X is given by,

P(Xx)=1-for x>0

=0                for x0

Step 2 of 3:

(a)

Here we have to find the probability that the lifetime of the bearing is more than 1 year.

That is,we have to find P(X>1)

P(X>1)=1-P(X1)

=1-[1-]

=

=

=0.4900

Thus,probability that the lifetime of bearing is more than 1 year is 0.4900.

Step 3 of 3

##### ISBN: 9780073401331

This full solution covers the following key subjects: bearing, Probability, lasts, years, less. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 17SE from chapter: 4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 17SE from 4 chapter was answered, more than 237 students have viewed the full step-by-step answer. The answer to “The lifetime of a bearing (in years) follows the Weibull distribution with parameters ? = 1.5 and ? = 0.8.a. What is the probability that a bearing lasts more than 1 year?________________b. What is the probability that a bearing lasts less than 2 years?” is broken down into a number of easy to follow steps, and 44 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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