The transmission on a particular model of car has a warranty for 40,000 miles. It is known that the

life of such a transmission has a normal distribution with a mean of 72,000 miles and a standard

deviation of 12,000 miles. Answer the following questions.

a) What percentage of the transmissions will fail before the end of the warranty period?

b) What percentage of the transmissions will be good for more than 100,000 miles?

c) What percentage of the transmissions will be good for 80,000 to 100,000 miles?