SOLUTION: Suppose a life insurance company sells a $250000 1-year term life insurance policy to a 20-year-old female for $260. According to the National Vital Statistics Repor
Algebra.Com
Question 1186128: Suppose a life insurance company sells a $250000 1-year term life insurance policy to a 20-year-old female for $260. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544 . The expected value of this policy to the insurance company is $146.00. What is the standard deviation of the value of the life insurance policy? Why is the value so high?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to calculate the standard deviation of the value of the life insurance policy and an explanation of why it's so high:
**1. Define the possible outcomes and their probabilities:**
* **Death:** The probability of death is 1 - 0.999544 = 0.000456. The payout is $250,000.
* **Survival:** The probability of survival is 0.999544. The "payout" (from the company's perspective) is the negative of the premium, or -$260.
**2. Calculate the squared deviations from the expected value:**
* **Death:** ($250,000 - $146)² = $249,854² ≈ 62,427,025,316
* **Survival:** (-$260 - $146)² = (-$406)² = 164,836
**3. Calculate the weighted average of the squared deviations (variance):**
Variance = (Probability of Death * Squared Deviation for Death) + (Probability of Survival * Squared Deviation for Survival)
Variance = (0.000456 * 62,427,025,316) + (0.999544 * 164,836)
Variance ≈ 28,474,831.54 + 164,758.33
Variance ≈ 28,639,589.87
**4. Calculate the standard deviation:**
Standard Deviation = √Variance
Standard Deviation ≈ √28,639,589.87
Standard Deviation ≈ $5,351.60
**Why is the standard deviation so high?**
The standard deviation is high because of the large difference in payouts between the two scenarios (death vs. survival). The payout in the case of death ($250,000) is significantly larger than the premium collected ($260). Even though the probability of death is small, the large payout creates a substantial variability in the possible values of the policy from the insurance company's perspective. This high variability is reflected in the large standard deviation.
RELATED QUESTIONS
Suppose a life insurance company sells a $300 comma 000 one-year term life... (answered by ikleyn)
Suppose a life insurance company sells a $190,000 one year term life insurance policy to (answered by Theo)
A life insurance company sells a $250,000 1-year term life insurance policy to a... (answered by solver91311)
A life insurance company sells a 150,000 one year term life insurance policy to a 35 year (answered by ewatrrr)
A 32 year old woman purchases a 100,000 term life insurance policy for an annual payment... (answered by stanbon)
A 37-year-old woman purchases a $100,000 term life insurance policy for an annual payment (answered by stanbon)
A 31-year-old woman purchases a 200,000 term life insurance policy for an annual payment (answered by ikleyn)
A 35 year old woman purchases a $100,000 term life insurance policy for an annual payment (answered by checkley71)
A 35-year-old woman purchases a $100,000 term life insurance policy for an annual payment (answered by stanbon)