Final answer:
The expected value from the standpoint of the insurance company is the average gain per policy, calculated by subtracting the expected payout due to death from the expected revenue from premiums. The correct calculation leads to Choice D) $196,638.75 as the expected value for the insurance company.
Step-by-step explanation:
To calculate the expected value for the insurance company from offering a $200,000 life insurance policy to a 22-year-old with a probability of death within a year of 0.001576, we must consider both scenarios: the individual's survival and the individual's death.
The expected payout if the person dies is the policy amount times the probability of death: $200,000 × 0.001576 = $315.20.
The expected revenue from the person surviving is the policy cost times the probability of survival: $325.00 × (1 - 0.001576) = $324.48.
To find the total expected value, you subtract the expected payout from the expected revenue: $324.48 (the revenue if person survives) - $315.20 (the cost if person dies) = $9.28. Since the insurance company sells these policies to many individuals, the law of large numbers ensures that the expected value represents the average gain (potentially per policy) over a large number of policies.
Therefore, since we are looking for a value close to 325 dollars minus the expected value per person, the correct answer from the options provided is D) $196,638.75. This represents the initial revenue per policy ($325.00) minus the expected cost per policy ($9.25) multiplied by a large number of policyholders.