An insurance company has a portfolio of 10,000 policies. Based on past data the company estimates that the probability of a claim on any one policy in a year is 0.003. It assumes no policy will generate more than one claim in a year. (a) Determine the approximate probability of more than 40 claims from the portfolio of 10,000 policies in a year. (4) (b) Determine an approximate equal-tailed interval into which the number of claims per year will fall with probability 0.95. (2) (c) In practice 42 claims were received in a particular year. A Director of the company complains about the range of estimates in part (b) being wrong.