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A manufacturer of microwave ovens is trying to determine the length of warranty...

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A manufacturer of microwave ovens is trying to determine the length of warranty period it should attach to its magnetron tube, the most critical component in the oven. Preliminary testing has shown that the length of life (in years), X, of a magnetron tube has an exponential probability distribution with mean 6.25.

What should the warranty period be if the manufacturer wants to replace only 27.5% of the tubes?

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