Machine repair time. [Note: This exercise refers to an optional section in Chapter 5.] An article in Industrial Engineering (Aug. 1990) discussed the importance of modeling machine downtime correctly in simulation studies. As an illustration, the researcher considered a single- machine-tool system with repair times (in minutes)

that can be modeled by an exponential distribution with u = 60. (See optional Section 5.6.) Of interest is the mean repair time x of a sample of 100 machine breakdowns.

a. Find E1x2 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.