At a customer service window the number of customers asking for assistance is a Poisson process with rate = 5 per hour.

(a) What is the probability that no customers would have to wait for assistance during a 12 minutes work-meeting for which the service window is closed?

(b) How many customers are expected to line up during the 12 minute break?

(c) What is the name of the distribution of the elapsed time between customers getting in line for assistance?

(d) What is the probability that the time elapsed between two customers is at least 12 minutes?