KleerCo supplies an under-hood, emissions control air pump to the automotive industry. The pump is vacuum powered and works while the engine is operating, cleaning the exhaust by pumping extra oxygen into the exhaust system. 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. The company’s current air pump lasts an average of 63,000 miles, with a standard deviation of 10,000 miles. The number of miles a pump operates before becoming ineffective has been found to be normally distributed.
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 at exactly 50,000 miles?
c. What percentage of the company’s pumps will fail between 40,000 and 55,000 miles?
d. For what number of miles does the probability become 80% that a randomly selected pump will no longer be effective?