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?
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ÃÂ 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?