An American tire manufacturer believes that the treadlife of a set of its snow tires can be described by a Normal distribution with a mean of 32,000 miles and a standard deviation of 2500 miles.

a. Tires that last less than 25,000 miles are eligible for exchange under the warranty offered by the company. Out of 100,000 tires sold, determine how many tires can be expected to be eligible for exchange.

b. In trying to decide whether or not to buy the tires, you want to know the probability that a set of these tires will last at least 35,000 miles. Determine this probability.

c. Determine the proportion of these sets of tires that can be expected to last between 30,000 and 35,000 miles.

d. Determine between what number of miles symmetrically distributed around the mean that 95% of the sets of tires last.

BETWEEN _________ AND _________

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 out of every 100 customers, determine what mileage the dealer can guarantee these tires to last.