The KleerCo company in Exercise 7.36 would like to design a more durable pump so that no more than 2% of original-equipment pumps are returned under free warranty, and the standard deviation continues to be 10,000 miles. What will the new average service life have to be in order for the new pump design to comply with this requirement?
In exercise
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.