Suppose a life insurance company sells a $260,000 1-year term life insurance policy to a 20-year-old female for $280. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.99954 Compute and interpret the expected value of this policy to the insurance company. The expected value is $. (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.) OA. The insurance company expects t make a maximum profit of $ OB. The insurance company expects to make a profit of $ Oc. The insurance company expects to make a minimum OD. The insurance company expects to make a profit of $ on every 20-year-old female it insures for 1 year. on every 20-year-old female it insures for 1 year. profit of $ on every 20-year-old female it insures for 1 month. on every 20-year-old female it insures for 1 month.
Suppose a life insurance company sells a $260,000 1-year term life insurance policy to a 20-year-old female for $280. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.99954 Compute and interpret the expected value of this policy to the insurance company. The expected value is $. (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.) OA. The insurance company expects t make a maximum profit of $ OB. The insurance company expects to make a profit of $ Oc. The insurance company expects to make a minimum OD. The insurance company expects to make a profit of $ on every 20-year-old female it insures for 1 year. on every 20-year-old female it insures for 1 year. profit of $ on every 20-year-old female it insures for 1 month. on every 20-year-old female it insures for 1 month.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Life Insurance Expected Value Calculation**
*Scenario:* A life insurance company sells a $260,000 1-year term life insurance policy to a 20-year-old female for $280. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. This exercise involves computing and interpreting the expected value of this policy for the insurance company.
**Computation of Expected Value:**
- **Expected Value Formula:**
\[
\text{Expected Value} = (\text{Profit if Survives} \times \text{Probability of Surviving}) + (\text{Loss if Dies} \times \text{Probability of Dying})
\]
- **Profit if Survives:** The company earns the premium, $280, because they do not have to pay out the policy.
- **Loss if Dies:** The company loses $259,720 (this is calculated as $280 - $260,000).
- **Probability Values:**
- Probability of surviving = 0.999544
- Probability of dying = 1 - 0.999544 = 0.000456
**Interpretations of the Expected Value:**
**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 maximum profit of $______ on every 20-year-old female it insures for 1 year.
- **B.** The insurance company expects to make a profit of $______ on every 20-year-old female it insures for 1 year.
- **C.** The insurance company expects to make a minimum profit of $______ on every 20-year-old female it insures for 1 month.
- **D.** The insurance company expects to make a profit of $______ on every 20-year-old female it insures for 1 month.
**Instructions:**
- Round your calculations to the nearest cent.
- Choose one interpretation (A, B, C, or D) for the computed expected value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac3be618-b645-4bd8-855b-808ff3fc18d4%2Fb3d0453a-4397-43b5-a447-0ef9a9782dfd%2Fyps4dm8_processed.png&w=3840&q=75)
Transcribed Image Text:**Life Insurance Expected Value Calculation**
*Scenario:* A life insurance company sells a $260,000 1-year term life insurance policy to a 20-year-old female for $280. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. This exercise involves computing and interpreting the expected value of this policy for the insurance company.
**Computation of Expected Value:**
- **Expected Value Formula:**
\[
\text{Expected Value} = (\text{Profit if Survives} \times \text{Probability of Surviving}) + (\text{Loss if Dies} \times \text{Probability of Dying})
\]
- **Profit if Survives:** The company earns the premium, $280, because they do not have to pay out the policy.
- **Loss if Dies:** The company loses $259,720 (this is calculated as $280 - $260,000).
- **Probability Values:**
- Probability of surviving = 0.999544
- Probability of dying = 1 - 0.999544 = 0.000456
**Interpretations of the Expected Value:**
**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 maximum profit of $______ on every 20-year-old female it insures for 1 year.
- **B.** The insurance company expects to make a profit of $______ on every 20-year-old female it insures for 1 year.
- **C.** The insurance company expects to make a minimum profit of $______ on every 20-year-old female it insures for 1 month.
- **D.** The insurance company expects to make a profit of $______ on every 20-year-old female it insures for 1 month.
**Instructions:**
- Round your calculations to the nearest cent.
- Choose one interpretation (A, B, C, or D) for the computed expected value.
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