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4. 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. Comment on the Director's complaint. (2)

4. 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. Comment on the Director's complaint. (2)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4. 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. Comment on the Director's complaint. (2)
Transcribed Image Text:4. 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. Comment on the Director's complaint. (2)
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