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$2.$ University X has a unique on$-$campus dispensary that provides medical care. On a typical working day, patients arrive at the dispensary at an average rate of $2$ patients per hour. There is one single nurse at the dispensary, and the average time required to give a consultation is $12$ minutes.

It is assumed that the service times can be described by the exponential distribution, and the arrival process by a Poisson distribution. You are requested to find: $($using EXCEL QM$)$

a$.$ The average time in line,

b$.$ The average number of patients in line,

c$.$ The average time in the system,

d$.$ The average number of patients in the system,

e$.$ The probability that the dispensary is empty,

f$.$ The utilization factor of the system.

Solution: