3. On a national highway, automobiles arrive for toll tax payment at an average rate of 3 in 5 minutes, according to the Poisson probability law. The attendant receives the tax in an average time of one minute per customer. The service (collecting the tax) time is exponentially distributed. You are required to determine:

(a) the probability of arrivals ofO through 5 customers in a 10-minute interval.

(b) the percentage of time the attendant at the toll gate shall be idle.

(c) the average time that the attendant is free in his 8-hour duty time.

(d) the probability of0 through 5 customers in the system.

(

e) the expected number of customers in the system.

(t) the expected number of customers waiting in the queue to pay tax.