A popcorn seller is very popular. The mean arrival rate of patrons 4 persons / minute and the service rate is 5 persons / minute. Modeling the system as an M/M/ 1 queuing system, determine the following performance measures:
a) Average length of queue
b) Average number of people in the system
c) Average wait time in the queue
d) Average wait time in the system
e) Percentage of time the server is idle