Question

A tire manufacturer states that a certain type of tire has a mean lifetime of 60,000 miles. Suppose lifetimes are normally distributed with standard deviation ơ = 3,500 miles.

1. Find the probability that if you buy one such tire, it will last only 57,000 or fewer miles. If you had this experience, is it particularly strong evidence that the tire is not as good as claimed?
2. The tire manufacturer offers a money back guarantee if the tire needs to be replaced before 65,000 miles. What is the probability a customer will get their money back?
3. The tire manufacturer only wants a return rate of 10%. At what mileage should they then offer a guarantee?

Answer 1

Define the standard random variable Z as Where X denotes lifetime

a) Using normal table we have

b) Required probability is

c) Let be the mileage such that

Then we know from normal table that

Hence

So the mileage should be 64,480