Insurance companies provide policies for people based on probabilities. Consider the following scenario. Palmetto Insurance Company offers term life insurance policies. Angelo is a 65 year old male in good health. He wants to take a out a $100,000 term life insurance policy until he turns 70. The probability of death in a given year is provided by the Social Security Actuarial Life Table (opens in a new window). cage 65 66 67 68 69 P(death at given age) 0.0159 0.0171 0.0185 0.0200 0.0216 This table is not a probability distribution because the probabilities do not add up to 1. Recall that a probability of 1 is a certainty. A person is not guaranteed to die between the ages of 65 and 70. This table displays the expected values for a person dying at a certain age. We can use those expected values to determine the expected cost if a person dies at a certain age. 1. What is the probability that Angelo will die in his 65th year? (Enter the decimal value.) 2. What is the expected cost to Palmetto Insurance Company? To find the expected cost to the company if a person dies during the policy period, multiply the probability of dying at the age times the policy payout. For this example, 100, 000(0.0159) = 1590. 3. What are the expected cost for ages 66, 67, 68, and 69? Complete the chart below. Age at Death 65 66 67 68 69 Expected Cost |$1,590 S 4. If Palmetto Insurance wants to make a profit of $1,000 above the expected total cost paid out from Angelo's death, how much should it charge for the policy? Find the sum of the expected costs for each age and the $1000 profit. The insurance should charge Angelo S for the policy