Normal Distribution

Question

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 10.9 years and a standard deviation of 2.4 years.

If the company wants to provide a warranty so that only 2.8% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty? 

warranty =  ? years

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Normal distribution with known

population mean,

mu = 10.9

population standard deviation

sigma = 2.4

Normal variate z has a value of

z = (x - mu)/sigma

x = measurement

We seek the z value for which only 2.8% = 0.028 exceeds the values from this distribution.

From a table of cumulative normal distribution values F(z)

(areas under the frequency distribution curve) we want the fraction

0.028 to be in the tail, where

z = 1.91 = (x - 10.9)/2.4

x = (1.91)(2.4) + 10.9 = 15.5 years

for the warranty.