The time to repair an equipment is known to be exponentially distributed with a mean of 45 min.
(a) What is the probability of the machine being repaired within half an hour?
(b) If the machine breaks down at 3 P.M. and a repairman is available immediately, what is the probability of the machine being available for production by the start of the next day? Assume that the repairman is available until 5 P.M.
(c) What is the standard deviation of the repair time?