Alpine Tire Company has determined from road tests that the mean mileage of its main product is 50,000 miles with a standard deviation of 5,000 miles, and that the collected data are normally distributed. Alpine wishes to offer a warrantee providing free replacement for any new tire that fails before the guaranteed mileage.

a. If Alpine wishes to replace no more than 10% of the tires, what should the guarantee mileage be?

b. In addition, the data collected indicate that the normal distribution is a reasonable assumption. What is the probability that the tire mileage will exceed 50,500miles?