JENN Inc. supplies under-hood emission control air pumps to the automative 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 traveled 50,000 miles, Federal emission regulations require that it be replaced at no cost to the vehicle owner. The company's current air pump lasts an average of 61,000 miles, with a standard deviation of 9,000 miles. The number of miles a pump operates before becoming ineffective has been found to follow a Normal distribution.
1. For the current pump design, what percentage of the company's pumps will have to be replaced at no charge to the vehicle owner? (show analysis for practice prob and show why)
2. What percentage of the company's pumps will fail at exactly 50,000 miles? (show analysis and why)
3. What percentage of the company's pumps will fail at mileage between 42,000 and 57,000? (show work/why)
4. For what number of miles does the probability become 80% that a randomly selected pump will no longer be effective? (show how assessed/why)
The solution uses probabilities an normal distributions to decide how many pumps will be replaced and when they will fail.