An insurance company charges $226 for a $50,000 life insurance policy for a 50 year-old female. The probability that such a female survives the year is 0.9969. Assume that the company sells 750 such policies to 50 year-old females, and it collects $169,5000 in policy payments. The company will make a profit if fewer than four of the 750 women die during the year.
What is the mean number of deaths in such groups of 750 females?
Using a Poisson distribution, find the probability that the company makes a profit from the 750 policies. Is that probability high enough so that the company is almost sure to make a profit?
- The mean number of deaths ______
- The probability that the company will make a profit is _____ (round to three decimals if needed)
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