## Normal Distribution Word Problem

"Suppose that the warranty period is extended to 24 months and it is pro-rated in that the customer recovers only the value of the time remaining to 24 months. For example, if a muffler fails at 22.5 months, then the time remaining to 24 months is only 1.5 months, and the customer receives 1.5/24 = .0625 of the value of a new muffler. If a muffler costs $64, this is worth$4. Moreover (and this is the point of the problem), of the mufflers that fail within the warranty period, most will fail by only a short amount of time.