show work Chapter04 sec4-5 HW: Problem 7 Previous Problem List Next (2 points) T

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Chapter04 sec4-5 HW: Problem 7 Previous Problem List Next (2 points) The lifetime of a certain battery is modeled with the Weibull distribution with a. What proportion of batteries will last longer than 9 hours? b. What proportion of batteries will last less than 4 hours? 0 c. Find the median lifetime of a battery 2.6 and 4.55 Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 2 times Your overall recorded score is 0% You have unlimited attemnts remainin

Explanation / Answer

we can solve this using the open source statistical package R

## greater than 9 hours
pweibull(9, shape = 2.6, scale = 4.55, lower.tail = FALSE)

## less than 4 hours

pweibull(4, shape = 2.6, scale = 4.55, lower.tail = TRUE)

## median life time is

2.6*(log(2))^(1/4.55)

The results are

> ## greater than 9 hours
> pweibull(9, shape = 2.6, scale = 4.55, lower.tail = FALSE)
[1] 0.002763766
> ## less than 4 hours
> pweibull(4, shape = 2.6, scale = 4.55, lower.tail = TRUE)
[1] 0.5109853
> ## median life time is
> 2.6*(log(2))^(1/4.55)
[1] 2.398777

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