12 An average of 40 jobs per day arrive at a factory. The time between arrivals of jobs is exponentially distributed.

The factory can process an average of 42 jobs per day, and the time to process a job is exponentially distributed.

a What is the probability that exactly 180 jobs arrive at the factory during a 5-day period?

b On the average, how long does it take before a job is completed (measured from the time the job arrives at the factory)?

c What fraction of the time is the factory idle?

d What is the probability that work on a job will begin within 2 days of its arrival at the factory?