Question: 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?