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 deviation of 2,500 miles. 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?

What is the name of the distribution that you used to model this problem?

What are the values of the parameters of this distribution?