F&G Industries manufactures a wash-down motor that is used in the food processing industry. The motor is marketed with a warranty that guarantees it will be replaced free of charge if it fails within the first 13,000 hours of operation. On average, F&G wash-down motors operate for 15,000 hours with a standard deviation of 1,250 hours before failing. The number of operating hours before failure is approximately normally distributed.
a. What is the probability that a wash-down motor will have to be replaced free of charge?
b. What percentage of F&G wash-down motors can be expected to operate for more than 17,500 hours?
c. If F&G wants to design a wash-down motor so that no more than 1% are replaced free of charge, what would the average hours of operation before failure have to be if the standard deviation remains at 1,250 hours?