There is only 1 copying machine in the student hostel of the polytechnic. Students arrive at the rate of 40 per hour(according to a Poisson distribution). Copying takes an average rate of 40 seconds or 90 per hour(according to an exponential distribution). Compute the following:

a. The percentage of time that the machine is used.

b. The average length of the queue.

c. The average number of students in the system

d. The average time spent waiting in the queue

e. The average time in the system

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