Question

I have problem with question 54 (Tires) from chapter 5 (The standard Deviation as a ruler and the normal model) fifth edition of Intro Stats (by De VEAUX/VELLEMAN/BOCK) . Please help me.

Question is:

A tire manufacturer believes that the treadlife of its snow tires can be described by a Normal model with a mean of 32,000 miles and standard deviation of 25000 miles.

1. If you buy one of these tires, would it be reasonable for you to hope it will last 40,000 miles? Explain.
2. Approximately what fraction of these tires can be expected to last than 30,000 miles?
3. Approximately what fraction of these tires can be expected to last between 30,000 and 35,000?
4. Estimate the IQR of the treadlives.
5. In planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tire fail to last a certain number of miles. However, the dealer does not want to take too big risk. If the dealer is willing to give refunds to no more than 1 of every 25 customers, for what mileage can he guarantee these tires to last?

Answer 1