Final answer:
The insurance company's expected value for selling a $12,000 life insurance policy for $465 to an 80-year-old male is a loss of $406.49 per policy.
Step-by-step explanation:
The question involves calculating the expected value for an insurance company when selling a life insurance policy to an 80-year-old male. The probability of death within a year for such a person is given as 0.069941. If the insurance policy is worth $12,000 and is sold for $465, we can calculate the expected value for the insurance company.
The expectation is calculated using the formula:
- E[X] = (probability of death) × (payout on death) + (probability of survival) × (net premium),
- where E[X] is the expectation,
- payout on death is the life insurance amount,
- and net premium is the amount the company gains if the person does not die.
Let's go step by step:
- Calculate the expected payout on death: 0.069941 × $12,000 = $839.29.
- Calculate the expected income from premiums: (1 - 0.069941) × $465 = $432.80.
- Subtract the expected payout from the expected income: $432.80 - $839.29 = -$406.49.
This negative value means that on average, the insurance company can expect to lose $406.49 per policy sold to an 80-year-old male for $465.