Tire Manufacturing: Normal Distribution and Standard Deviation

A tire manufacturer believes that the tread life of its snow tires can be described as a normal distributionwith a meanof 32,000 miles and a standard deviationof 2500 miles.

a. If you buy a set of these tires, would it be reasonable to expect they will last 40,000 miles? What do you base your decision on?

b. What percentage of these tires can be expected to last less than 30,000 miles?

c. What percentage of these tires can be expected to last between 30,000 and 35,000 miles?

d. Estimate the IQR of the tires’ tread life.

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 to big a risk. If the dealer is only willing to give a refund to no more 2% of the customers, for what mileage can he guarantee these tires to last?

This is a response finding the percentage of tires that can last varying distances. Based on those responses, the company finds creates a marketing strategy.