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Someone suggests that the lifetime T (in days) of a

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

Solution for problem 12E 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 12E

Someone suggests that the lifetime T (in days) of a certain component can be modeled with the Weibull distribution with parameters \(\alpha\) = 3 and \(\beta\) = 0.01.

a. If this model is correct, what is P(T ≤ 1)?

b. Based on the answer to part (a), if the model is correct, would one day be an unusually short lifetime? Explain.

c. If you observed a component that lasted one day, would you find this model to be plausible? Explain.

d. If this model is correct, what isP(T ≤ 90)?

e. Based on the answer to part (d), if the model is correct, would 90 days be an unusually short lifetime? An unusually long lifetime? Explain.

f. If you observed a component that lasted 90 days, would you find this model to be plausible? Explain.

Equation transcription:

Text transcription:

\alpha

\beta

Step-by-Step Solution:

Solution:

Step 1 of 4:

The lifetime  T of a certain component modeled with the weibull distribution with parameters and = 0.01.

We have to find

  1.  P(, if the model is correct.
  2. Is one day be an unusually short lifetime, if the model is correct.
  3. Is this model  is reasonable according to the observation.
  4. P(, if the model is correct.
  5.  Is 90 days be an unusually short lifetime or not.
  6. Is this model is reasonable according to the observation.

Step 2 of 4

Chapter 4.8, Problem 12E is Solved
Step 3 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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