Question

suppose a life insurance company sells a $200,000 1 - year term life insurance policy to a 20 - year - old female for $320. 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. the expected value is $ (round to the nearest cent as needed.)

Explanation:

Step1: Determine the two possible outcomes and their probabilities

• If the female survives the year:
• The insurance company's gain is \(320\) dollars (the premium it received).
• Probability \(P_1 = 0.999544\)
• If the female does not survive the year:
• The insurance company's gain is \(320 - 200000=- 199680\) dollars (it received \(320\) but has to pay out \(200000\)).
• Probability \(P_2=1 - 0.999544 = 0.000456\)

Step2: Use the expected - value formula \(E(X)=\sum_{i = 1}^{n}x_iP(x_i)\)

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Answer:

The expected value is \(\$228.80\). This means that, on average, for each such policy sold to a 20 - year - old female, the insurance company can expect to make a profit of approximately \(\$228.80\) per policy in the long run.