The lifetime of a certain brand of tires is approximately normally distributed, with a mean of 45,000 miles and a standard deviation of 2,500 miles. The tires carry a warranty for 40,000 miles. Answer the question by computing the requested values in three ways in each of parts a-c:

1. a) What proportion of the tires will fail before the warranty expires?
2. b) What proportion of the tires will fail after the warranty expires but before they have lasted for 41,000 miles?
3. c) What should the warranty be if the company wants no more than a 1% failure rate?