Question

A company that produces an expensive stereo component is considering offering a warranty on the component. Suppose the population of lifetimes of the components is a normal distribution with a mean of 88 months and a standard deviation of 7 months. If the company wants no more than 2% of the components to wear out before they reach the warranty date, what number of months should be used for the warranty? (Enter your answer as a whole number.)

Answer 1

Solution :

mean = = 88 months

standard deviation = =7 months

Using standard normal table,

P(Z > z) = 2%

1 - P(Z < z) = 0.02

P(Z < z) = 1 - 0.02 = 0.98

P(Z < 2.054) = 0.98

z = 2.05

Using z-score formula,

x = z * +

x = 2.05 * 7 + 88 = 102.35

The warranty   for used 102 months