Suppose a life insurance company sells a \( \$ 190,000 \) 1-year term life insurance policy to a 20 -year-old female for \( \$ 340 \). 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.)

To compute the expected value of the insurance policy, we need to consider both outcomes: the female survives the year and the female does not survive the year. 1. **Probability that the female survives the year**: 0.999544 - If she survives, the company keeps the premium, which is \( \$340 \). 2. **Probability that the female does not survive the year**: \( 1 - 0.999544 = 0.000456 \) - If she does not survive, the company pays out \( \$190,000 \) and keeps \( \$340 \), resulting in a loss of \( \$190,000 - \$340 = \$189,660 \). Now we can calculate the expected value (EV): \[ EV = (Probability\ of\ survival \times Profit) + (Probability\ of\ death \times Loss) \] \[ EV = (0.999544 \times 340) + (0.000456 \times -189660) \] \[ EV = (339.27) + (-86.23) \] \[ EV = 339.27 - 86.23 = 253.04 \] Thus, the expected value is \( \$253.04 \). The expected value of \( \$253.04 \) means that, on average, the insurance company can expect to gain this amount per policy sold under these conditions. It reflects the balance of risks associated with the life insurance policy.