Question

The operation life of an Arctic Air portable cooler is normally distributed with mean 75 months and standard deviation 9 months. The manufacture will replace any cooler that breaks during that guarantee period. If the guarantee period is for five years, what percent of the coolers will the manufacture have to replace? How long should the guarantee run if the manufacture does not want to replace more than 2.5 % of the coolers?

Answer 1

Solution :

Given that,  

mean = = 75

standard deviation = = 9

Using standard normal table ,

P(Z > z) = 2.5%

1 - P(Z < z) = 0.025

P(Z < z) = 1 - 0.025 = 0.975

P(Z < 1.96) = 0.975

z = 1.96

Using z-score formula,

x = z * +

x = 1.96 * 9 + 75 = 92.64

It should the guarantee run if the manufacture does not want to replace more than 2.5 % of the coolers is 92.64