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 86 months and a standard deviation of 9 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 :

Given that,

mean = = 86

standard deviation = = 9

Using standard normal table,

P( Z > z) = 2%

P(Z > z) = 0.02

1 - P( Z < z) = 0.02

P(Z < z) = 1 - 0.02

P(Z < z) = 0.98

z = 2.05

Using z-score formula,

x = z * +

x = 2.05 * 9+ 86

x =104.45

104 of months should be used for the warranty.