Question

A tire manufacturer believes that the life of its tires follow a normal distribution with a mean of 46,000 miles and a standard deviation of 4,000 miles. What mileage can he guarantee each tire to last so that 99% of the tires last longer than the guaranteed lifetime?

Answer 1

Solution:

Given: A tire manufacturer believes that the life of its tires follow a normal distribution with a mean of miles and a standard deviation of miles.

We have to find x = guaranteed lifetime so that:

P( X > x ) = 99%

P( X > x ) = 0.99

thus find z value such that:

P( Z > z ) = 0.99

that is find

P( Z < z) = 1 - P( Z > z )

P( Z < z) = 1 - 0.99

P( Z < z) = 0.01

look in z table for area = 0.0100 or its closest area and find z value.

Area 0.0099 is closest to 0.0100 and it corresponds to -2.3 and 0.03

thus z = -2.33

Now use following formula to find x value:

Thus 36,680 miles he can guarantee each tire to last so that 99% of the tires last longer than the guaranteed lifetime