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A new shopping mall is considering setting up an information desk manned by one employee.

Based on information obtained from similar information desks, it is believed that people will arrive

at the desk at the rate of $15$ per hour. It takes an average of $3$ minutes to answer a question. It is

assumed that arrivals rate and answer times are exponentially distributed.

a$)$ What is the notation of the system?

b$)$ Find the probability that the employee is idle.

c$)$ Find the proportion of the time that the employee is busy.

d$)$ Find the average number of people receiving and waiting to receive information.

e$)$ Find the average number of people waiting in line to get information.

f$)$ Find the average time a person seeking information spends at the desk.