Question

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 17 years and a standard deviation of 2.2 years.

If the company wants to provide a warranty so that only 4.1% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?
warranty =  years

Answer 1

Given,

= 17 , = 2.2

We convert this to standard normal as

P(X < x) = P(Z < (X - ) / )

We have to calculate X such that P(X < x) = 0.041

P(Z > x - ) / ) = 0.041

P(Z < x - ) / ) = 0.959

From Z table, Z-score for the probability of 0.959 is 1.7392

So,

(x - ) / = 1.7392

( x - 17) / 2.2 = 1.7392

X = 20.83 years.