A company 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

10,000

hours of operation. On average, the wash-down motors operate for

13,000

hours with a standard deviation of

2,950

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 wash-down motors can be expected to operate for more than 18,900 hours?
c.	If the company 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 2,950 hours?