There is a 0.9986 probability a randomly selected 30-year old male live through the year. An insurance company called, None-of-your-Business, charges \$161 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out \$100,000 as a death benefit. Assume that the company sells 1300 such policies to 30-year-old males, so it collects \$209,300 in policy payments. The company will make a profit if the number of deaths in this group is two or fewer.

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a. What is the mean number of deaths in such groups of 1300 males?

b. Use the Poisson distribution to find the probability that the company make a profit from the 1300 policies.

c. Use the binomial distribution to find the probability that the company makes a profit from the 1300 policies. Compare this result to that from part b.

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