# The lifetime of a certain battery is modeled with the

## Problem 10E Chapter 4.8

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 10E

The lifetime of a certain battery is modeled with the Weibull distribution with α= 2 and  =β 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?

Step-by-Step 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.

Step 2 of 3:

Let T is the lifetime of batteries which follows weibull distribution with parameters .

So the pdf of T is

f(t) =

=  (2 ) (0.1

And the density function of T is

F(t)  =   P(

=   1-

=  1-

1- F(t)  =

Proportion of batteries will last longer than 10 hours.

P(T>10)  =  1- P(T)

P() = F(10)

=  1-

=  1 -

=  0.6321.

P(T>10)    = 1- 0.6321

=   0.3678

Therefore the probability P(T>10) is 0.3678.

(b)  proportion of batteries will last less than 5 hours.

P(T<5) =  P(

=   1-

=    1- 0.7788

=   0.2211

Therefore the probability that batteries will last less than 5 hours is 0.2211.

Step 3 of 3

##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4th. The answer to “The lifetime of a certain battery is modeled with the Weibull distribution with ?= 2 and =? 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?” is broken down into a number of easy to follow steps, and 65 words. This full solution covers the following key subjects: batteries, proportion, longer, Hazard, exercise. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 10E from chapter: 4.8 was answered by Patricia, our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 10E from 4.8 chapter was answered, more than 363 students have viewed the full step-by-step answer.

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