Question

Company XYZ know that replacement times for the DVD players it produces are normally distributed with a mean of 9.2 years and a standard deviation of 1 years.

If the company wants to provide a warranty so that only 1.4% of the DVD players will be replaced before the warranty expires, what is the time length of the warranty?
warranty = ? years

Answer 1

Solution :

mean = = 9.2

standard deviation = = 1

Using standard normal table,

P(Z > z) = 1.4 %

1 - P(Z < z) = 0.014

P(Z < z) = 1 - 0.014 = 0.986

P(Z < 2.197) = 0.986

z = 2.197

Using z-score formula,

x = z * +

x = 2.197 * 1 + 9.2

= 11.397

= 11.4

The time length of the warranty is 11.4 years.

Minimum amount = 23.956