WangCo supplies an under-hood, emissions control air pump to the automotive industry.The company's current air pump lasts an average of 63,000 miles, with a standard deviation of 10,000 miles.Assume that the number of miles a pump operates before becoming ineffective to be normally distributed. If a pump fails before the vehicle in which it is installed has covered 50,000 miles, federal emissions regulations require that it be replaced at no cost to the vehicle owner.

(a)For the current pump design, what percentage of the company's pumps will have to be replaced at no charge to the consumer?

(b)What percentage of the company's pumps will fail between 45,000 and 55,000 miles?

(c) For what number of miles does the probability become 85% that a randomly selected pump will no longer be effective?