C. 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 policy in a year is 0.003. It assumes no policy will generate more that one claim in a year. (i) Determine the approximate probability of more than 40 claims from the portfolio of 10,000 policies in a year. (ii) Determine an approximate equal tailed interval into which the number of claims per year will fall with the probability 0.95. In practice 42 claims were received in a particular year. A director of the company complains about the range of estimates in part (ii) being wrong. (i) Comment on the director's complaint.
C. 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 policy in a year is 0.003. It assumes no policy will generate more that one claim in a year. (i) Determine the approximate probability of more than 40 claims from the portfolio of 10,000 policies in a year. (ii) Determine an approximate equal tailed interval into which the number of claims per year will fall with the probability 0.95. In practice 42 claims were received in a particular year. A director of the company complains about the range of estimates in part (ii) being wrong. (i) Comment on the director's complaint.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:C. 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 policy in a year is 0.003.
It assumes no policy will generate more that one claim in a year.
(i) Determine the approximate probability of more than 40 claims from the
portfolio of 10,000 policies in a year.
(ii) Determine an approximate equal tailed interval into which the number of
claims per year will fall with the probability 0.95.
In practice 42 claims were received in a particular year. A director of the
company complains about the range of estimates in part (ii) being wrong.
(i) Comment on the director's complaint.
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