A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 10 per hour. It takes an average of three minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed.

(a) Find the probability that the employee is idle.

(b) Find the proportion of time that the employee is busy.

(c) Find the average number of people receiving and waiting to receive information.

(d) Find the average number of people waiting in line to get information.

(e) Find the average time a person seeking information spends at the desk.

(f) Find the expected time a person spends waiting in line to have his question answered.