I'm asked this question:
"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.
"Of all the mufflers that fail within 24 months, what proportion of them have failures in the interval (20 months, 24 months)?"
I'm confused because, if the mufflers that fail within the warranty time mostly fail within a short period of time, doesn't this contradict that the distribution is approximately normal? Doesn't that make the calculation impossible?