The Computer Help Desk at Averill University Receives an Average

The computer help desk at Averill University receives an average of 40 calls per hour and calls come in according to a Poisson distribution. The average time a technician takes to diagnose a problem is three minutes and twenty seconds, and the service time follows an exponential distribution. For 60% of the callers the diagnosis is satisfactory, but for 40% of the callers, the technician must transfer the call to a specialist. The time a
caller speaks to a specialist follows an exponential distribution
with a mean of five minutes. For ninety five percent of callers
transferred to a specialist, the problem is solved, but five percent
of callers will need an on-site visit from a service technician.
The average time a technician takes to fix a computer on-site is
forty minutes with a standard deviation of ten minutes.

The help desk operation has three technicians answering the incoming
calls, two specialists handling calls, and one on-site technician.
If a caller needs to have on-site service, determine the average
time it will take to have the service completed form the time the
initial call is made.