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The lifetime of a certain battery is modeled with the
Chapter 4, Problem 10E(choose chapter or problem)
The lifetime of a certain battery is modeled with the Weibull distribution with \(\alpha\) = 2 and \(\beta\) = 0.1.
a. What proportion of batteries will last longer than 10 hours?
b. What proportion of batteries will last less than 5 hours?
c. What proportion of batteries will last longer than 20 hours?
d. The hazard function is defined in Exercise 8. What is the hazard at t = 10 hours?
Equation transcription:
Text transcription:
\alpha
\beta
Questions & Answers
QUESTION:
The lifetime of a certain battery is modeled with the Weibull distribution with \(\alpha\) = 2 and \(\beta\) = 0.1.
a. What proportion of batteries will last longer than 10 hours?
b. What proportion of batteries will last less than 5 hours?
c. What proportion of batteries will last longer than 20 hours?
d. The hazard function is defined in Exercise 8. What is the hazard at t = 10 hours?
Equation transcription:
Text transcription:
\alpha
\beta
ANSWER:
Solution:
Step 1 of 3:
The lifetime of a battery modeled with weibull distribution with parameters .
We have to find
- The proportion of batteries will last longer than 10 hours.
- The proportion of batteries will last less than 5 hours.
- The proportion of batteries will last longer than 20 hours.
-
If the hazard function of lifetime (T) is h(t) =
, then what is the hazard at t=10 hours.