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Suppose a life insurance company sells a ​$260,000 ​1-year term life insurance policy to a 20​-year-old female for ​$220. According to the National Vital Statistics​ Report, 58(21), the probability that the female survives the year is 0.999544. Compute and interpret the expected value of this policy to the insurance company.

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coolstick

Answer:

$101.44

Step-by-step explanation:

To calculate expected value, we can multiply each outcome by its probability. The probability that the female will pay is 100%, so to start, the expected value is (100%) * $220 = 1 * $220 = $220

Next, the only way the insurance loses or gains money outside of this value is if the female dies. The probability of this happening is 1 - 0.999544 (the probability that the female survives) = 0.000456 . Therefore, the expected value that the insurance company will pay to the woman is

(260000) * (0.000456) = 118.56

Overall, the insurance company is expected to gain $220 from the woman and lose $118.56. Adding these two up, we get

220-118.56 = $101.44 as the overall expected value of the policy to the insurance company

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