Part 1 of 2 points Points: 0 of 1 Save Suppose a life insurance company sells a $\$ 170,000$ 1-year term life insurance policy to a 20 -year-old female for $\$ 190$. 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 $\$ \square$. (Round to the nearest cent as needed.) View an example Get more help - Clear all Check answer

Step 1 ：Define the probabilities and outcomes. The probability that the female survives the year is 0.999544, so the probability that she does not survive is \(1 - 0.999544 = 0.000456\). If she survives, the insurance company makes a profit of $190. If she does not survive, the company loses $170,000 but gains the $190 premium, for a total profit of \(-\$170,000 + \$190 = -\$169,810\).

Step 2 ：Calculate the expected value. The expected value is the sum of the products of each outcome and its probability. So, the expected value is \((\$190 \times 0.999544) + (-\$169,810 \times 0.000456) = \$112.48\).

Step 3 ：The expected value is the average amount the insurance company expects to earn per policy. So, on average, the insurance company expects to earn \$112.48 per policy sold.