An insurance company has a portfolio of 12,000 policies. Based on past data the company

estimates that the probability of a claim on any one policy in a year is 0.0045. It assumes

no policy will generate more than one claim in a year.

(a) Determine the approximate probability of more than 64 claims from the portfolio

of 12,000 policies in a year.

(b) Determine an approximate equal-tailed interval into which the number of claims

per year will fall with probability 0.95.

(c) In practice 70 claims were received in a particular year. A Director of the company

complains about the range of estimates in part (b) being wrong.

Comment on the Director's complaint.