A short-term insurance company receives seven motor vehicle claims, on average, per day. Assume that the daily claims rate follows a Poisson process.
(a) What is the probability that on a given day no more than five motor vehicle claims will be received?
(b) How likely is it that either six or nine motor vehicle claims will be received on a given day?
(c) What is the chance that more than 20 motor vehicle claims will be received by the company over any two-day period? (Hint: Refer to the 'word of caution' in section 5.4.)
Note: Calculate all the probabilities using the Poisson formula and then the Excel function POISSON.