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 β = 60. Of interest is the mean repair time, Y̅, of a sample of 100 machine breakdowns.

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

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

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