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Someone suggests that the lifetime T (in days) of a
Chapter 4, Problem 12E(choose chapter or problem)
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
Questions & Answers
QUESTION:
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
ANSWER: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
- P(, if the model is correct.
- Is one day be an unusually short lifetime, if the model is correct.
- Is this model is reasonable according to the observation.
- P(, if the model is correct.
- Is 90 days be an unusually short lifetime or not.
- Is this model is reasonable according to the observation.