Answer to Question #342624 in Statistics and Probability for Jose

Question

The lifetimes of a certain type of electrical components are distributed with a mean of 800 hours and standard deviation of 160 hours.If the manufacturer wishes to replace only 1 percent of the component that have the shortest life .what value should be used as the guaranteed lifetime

Answer 1

$$P(X<x)=P(Z<\dfrac{x-800}{160})=0.01$$

$$\dfrac{x-800}{160}=-2.3263$$

$$x=800-160(2.3263)$$

$$x=427.8\ hours$$