(i) A total number of 194 tornadoes hit a city in one year. Let X= total number of tornadoes that hit the city in one year.

(a) What probability distribution would you use to model X? Explain your answer in two sentences.

Exponential distribution with mean of 194.

(b) What is the probability (to 4 d.p.) that at most 80 tornadoes hit the city within half a year?

ii. The Ferries at Lyttleton Harbour are expected to arrive from Diamond Harbour every 30 minutes. Let X be the random variable for the number of minutes that somebody arriving at the wharf at a random time will have to wait before a ferry arrives.

(a) What probability distribution would you use to model X? Explain your choice in one or two sentences.

(b) Calculate the expected value of and the standard deviation of this distribution (to 3 d.p.).