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.
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.