Question 1186128
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.