Customers arrive at a bank counter manned by a single cashier according to Poisson distribution with mean arrival rate 6 customers/hour. The cashier attends the customers on first come first serve basis at an average rate of 10 customers/hour with the service time exponentially distributed. Find:
a) the probability of the number of arrivals (0 through 5) during (i) 15-minute interval, (ii) 30-minute interval.
b) the probability that the queuing system is idle.
c) the probability associated with the number of customers (0 through 5) in the queuing system.
d) the probability that there are more than 3 customers in the queuing system.
e) the time a customer should spend in queue.
f) the time a customer spends before leaving the bank counter.