The importance of modeling machine downtime correctly in simulation studies was discussed in Industrial Engineering (Aug. 1990).The paper presented simulation results for a single-machine-tool system with the following properties:

The interarrival times of jobs are exponentially distributed with a mean of 1.25 minutes The amount of time the machine operates before breaking down is exponentially distributed with a mean of 540 minutes

a. Find the probability that two jobs arrive.for processing at most one minute apart.

b. Find the probability that the machine operates for at least 720 minutes (12 hours) before breaking down.