12. Vacuum tubes produced at a certain plant are assumed to have an underlying exponential life distribution

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12. Vacuum tubes produced at a certain plant are assumed to have an underlying exponential life distribution having an unknown mean θ. To estimate θ it has been decided to put a certain number n of tubes on test and to stop the test at the 10th failure. If the plant officials want the mean length of the testing period to be 3 hours when the value of θ is θ = 20, approximately how large should n be?

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