Question

suppose a life insurance company sells a $220,000 1 - year term life insurance policy to a 20 - year - old female for $300 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: Define the two possible outcomes

Let \(X\) be the profit of the insurance company.
If the female survives (\(P(X = 300)=0.999544\)), the company's profit is \(300\) (the premium).
If the female does not survive (\(P(X=300 - 220000)=1 - 0.999544=0.000456\)), the company's profit is \(300-220000=- 219700\)

Step2: Use the expected - value formula

The expected - value formula is \(E(X)=\sum_{i}x_ip_i\)

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Answer:

\(199.68\)

Interpretation: On average, for each such policy sold, the insurance company can expect to make a profit of approximately \(\$199.68\) per policy in the long run.