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Chapter 8: Q. 8.14 (page 391)

A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure. If the mean lifetime of this type of component is 100 hours and its standard deviation is 30 hours, how many of these components must be in stock so that the probability that the system is in continual operation for the next 2000 hours is at least 0.95?

Short Answer

Expert verified

n鈮�23

Step by step solution

01

Given information

饾渿=100and饾湈=30

We need to find n.

Let pbe the probability they will last for atleast 2000 hours.

02

Fomulation

p=P鈭�Xii=1n鈮�2000鈮�PZ鈮�2000-100n30n

where Z is a standard normal random variable.

03

Calculating n

We know that

P(Z>-1.64)=0.95鈬�2000-100n30n鈮�-1.64鈬�2000-100n鈮�-49.2n

Upon using calculator, we get

n鈮�23.

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