Question: An article in Industrial Engineering August 1990 discussed the importance

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.

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