p(15) = 0.1024, or about 1 chance in 10.Explanation
The rate is 0.0030 for one man, or 15 for 5,000 men. We are taking men aged 42 in batches of 5,000, and we thus use the r = 15 column of the Poisson Table. We there learn that the chance of paying off on exactly 15 of the 15,000 policies is 0.1024. In typical Poisson fashion, for whole number r, we find that the chance of paying off on exactly r - 1 or 14 of the policies is the same: p(14) = 0.1024.
This is not really a rate problem (which is to say, not properly a Poisson problem), but a Binomial problem. The insured men who die in the year in question are the ones on whom the problem focuses, but the ones who don't die also exist - the company has on file names, addresses, and blood pressure readings for each and every one of them. If we can specify how many of them have not died in a given period, and we can, then by definition we are not really in Poisson territory.
Statistics is Copyright © 2001- by E Bruce Brooks
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