a) Find the probability of the number of arrivals (0-5) during i) a 15 minute interval and ii) a 30 minute interval. b) Probability that the system is idle. [3 Marks] [3 Marks] c) Calculate the expected number of customers in the tailor shop. [3 Marks] d) Compute the calculate the expected waiting time in the queue. [3 Marks] e) Derive the expected number of customers in the queue. [3 Marks] A tailor specializes in ladies dresses. The number of customers approaching the tailor appear to be Poison distributed with a mean of six customers per hour. The tailor attends to customers on a first-come-first-served basis and the customers wait if need be. The tailor can attend to the customers at an average rate of ten customers per hour with service time exponentially distributed.