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Inverse probability based on the Normal distribution.

In establishing warranty on TV 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 TV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where must the warranty limits be set so that only 10 percent of the TVs need repairs at the manufacturer's expense?

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