In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean
number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?
Let X be the number of months until repairs are needed. From the question, we need to find a value A so that
Note that X follows a normal ...
This solution contains a detailed explanation of computing the warranty limits using a normal distribution.