Suppose a life insurance company sells a \( \$ 300,0001 \)-year term life insurance policy to a 20 -year-old female for \( \$ 210 \). According to the National Vital Statistics Report, 58 ( 21 ), the probability that the female survives the year is 0999544 Compute and interpret the expected value of this policy to the insurance company. The expected value is \( \$ 73.20 \) (Round to the nearest cent as needed.) Which of the following interpretations of the expected value is correct? Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest cent as needed) A. The insurance company expects to make a profit of \( \$ \square \) on every 20 -year-old female it insures for 1 year. B. The insurance company expects to make a minimurn profit of \( \$ \square \) on every 20 -year-old female it insures for 1 month. O C. The insurance company expects to make a profit of \( \$ \square \) on every 20 -year-old female it insures for 1 month. O D. The insurance company expects to make a maximum profit of \( \$ \square \) on every 20 -year-old female it insures for 1 year
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The expected value of \( \$ 73.20 \) indicates the average profit the insurance company anticipates from insuring a 20-year-old female for one year. Since the premium collected is \( \$ 210 \) and the payout in case of a claim is \( \$ 300,000 \), this expected value reflects a balance between the probabilities of survival and death within that year. The company expects that on average, for each policy sold to this demographic, they will profit approximately \( \$ 73.20 \) if the same scenario is repeated numerous times. Therefore, the correct interpretation of the expected value is: **A. The insurance company expects to make a profit of \( \$ 73.20 \) on every 20-year-old female it insures for 1 year.**
