Tire company
A Tire manufacturer believes that the tread life of its snow tires can be described by a Normal model with a mean of 32,000 miles and a standard devia- tion of 2500 miles.
a) If you buy a set of these tires, would it be reasonable for you to hope that they'll last 40,000 miles? Explain.
b) Approximately what fraction of these tires can be ex- pected to last less than 30,000 miles?
c) Approximately what fraction of these tires can be ex- pected to last between 30,000 and 35,000 miles?
d) Estimate the IQR for these data.
e) In planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the dealer does not want to take too big a 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?