Customers arrive to the bank branch according to exponential distribution with the mean of 5 minutes. The bank opens at 9:00 a.m. and has three tellers
(a) Determine the probability that more than one customer arrive to the bank in half an hour?
(b) Determine the probability that all of them will be idle during the first 15 minutes of operation?
(c) Determine the probability that at least two tellers are busy during the first 30 minutes of operation?
(d) The bank has 10 branches in the greater Philadelphia area, what is the probability that more than 3 branches have at least two tellers busy during the first 30 minutes of operation?