During an eight-hour work day, starting from 9am, customers of a company arrive at a Poisson rate of two per hour.

(a) Assume that during the period from 10 am to 11 am, no customers arrived. Find the probability that during the next half an hour there will be no customers either.

(b) Assume that the fifteenth customer has arrived at 4 pm. (i) What is the probability that the seventeenth customer will come in less than one hour? (ii) Suppose that customers may arrive after the office is closed. The clerk of the company decides to wait for the seventeenth customer after the work day is over. What is the expected waiting time?
How long will the clerk wait for the seventeenth customer on the average if she/he does not work after hours and leaves at 5 pm?