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-machine-tool system with repair times (in minutes) that can be modeled by an exponential distribution with θ = 60. (See optional Section 5.6.) Of interest is the mean repair time x of a sample of 100 machine breakdowns.
a. Find E(x-bar) and the variance of x-bar.
b. What probability distribution provides the best model of the sampling distribution of x-bar? Why?
c. Calculate the probability that the mean repair time x-bar is no longer than 30 minutes.