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The mean time between failures (MTBF) of a hydraulic press is to be estimated assuming that the time between failures (TBF) is exponentially distributed. A foreman observes that the chance that the TBF is more than 72 hours is 50%, and he quotes 72 hours as the MTBF. a. Is the foreman right? If not, what is the MTBF? b. If the MTBF is indeed 72 hours, 50% of the time the TBF will be more than how many hours? c. Why is the mean of an exponential distribution larger than its median?

The mean time between failures (MTBF) of a hydraulic press is to be estimated assuming that the time between failures (TBF) is exponentially distributed. A foreman observes that the chance that the TBF is more than 72 hours is 50%, and he quotes 72 hours as the MTBF.

a. Is the foreman right? If not, what is the MTBF?

b. If the MTBF is indeed 72 hours, 50% of the time the TBF will be more than how many hours?

c. Why is the mean of an exponential distribution larger than its median?

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