Suppose that the time between emergency calls to a small suburban fire station follows an exponential distribution with an average rate of 1.8 calls per day. i. Phil the fireman has just clocked on. What is the chance of a call in the next 15 minutes.[2 marks] ii. Phil has nearly finished his shift: 15 minutes to go. There has been no call during his shift so far. What is the chance of a call in the next 15 minutes?[2 marks] iii. Judy works a 10 hour shift, Mondays to Thursdays. What is the probability that she has no calls in a shift?[2 marks] iv. What is the probability that she has no calls in four successive days?[2 marks] v. Judy is talking about her job: "in 10% of shifts there's a call in the first hours of the shift". What is to one decimal place?[2 marks]