A non-profit organization plans to offer a life insurance service. Participants agree to a five-year contract in which they pay the organization a yearly fee. The fee does not change over the course of the contract. If the policy holder dies during the five-year period, the organization will pay $100,000 to her family and there will be no more yearly fee. The probabilities of death at ages 60, 61, 62, 63, and 64 for a US woman on her 60th birthday are given inTable 11.15.

For example, on her 60th birthday a woman will have a 0.82% chance of dying at the age of 62.
(a) Let X be the organization€™s total profit, in dollars, five years after selling a contract to a woman on her 60th birthday. Write the probability distribution of X, where the values of X are given in terms of the yearly fee c.
(b) Write the mean of X in terms of c.
(c) What yearly fee should the organization charge 60-year-old women if they hope to break even? (The organization can expect to break even if they have a mean profit of $0.)

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61 Age Probability 0.00696 0.00756 0.00820 0.00885 0.00950 60 62 63 64