72 Machine repair time. An article in Industrial Engineering

(August 1990) discussed the importance of modeling machine downtime correctly in simulation studies. As an illustration, the researcher considered a single-machinetool system with repair times (in minutes) that can be modeled by an exponential distribution with u = 60. Of interest is the mean repair time x of a sample of 100 machine breakdowns

a. Find E(x) and the variance of x.

b. What probability distribution provides the best model of the sampling distribution of x ? Why?

c. Calculate the probability that the mean repair time x is no longer than 30 minutes.