Problem $7-24($Algo$)$

An office employs several clerks who create documents, and one operator who enters the document information in a computer system. The group creates documents at a rate of $22$ per hour. The operator can enter the information with an average exponentially distributed time of $2$ minutes. Assume the population is infinite, arrivals are Poisson, and queue length is infinite with the FCFS discipline.

Calculate the percentage utilization of the operator.

Note: Round your answer to $2$ decimal places.

Calculate the average number of documents in the system.

Note: Round your answer to $1$ decimal place.

Calculate the average time in the system.

Note: Round your answer to $1$ decimal place.

Calculate the probability of four or more documents being in the system.

Note: Round your intermediate calculations to $3$ decimal places and final answer to $1$ decimal place.

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