Calls arrive at a call centre according to a Poisson process with rate six per hour. (a) Amy starts work at the call centre. What is the probability that she has to wait for more than 5 minutes before the first call arrives? [5] (b) Bill arrives 20 minutes after Amy. What is the probability that Amy has to wait more than 5 minutes before the first call but at least 3 calls arrive between Amy and Bill arriving? [7] (c) What is the distribution of the time taken for 3 calls to arrive