Answer:
σₓ is approximately $316.07
Explanation:
The given parameters are;
The annual cost of the insurance policy = $60
The amount of payout the company makes = $10,000 for theft
The probability of theft in the area = 0.001
From the given data, we have
The formula for mean, μₓ = ∑[x · P(x)]
μₓ = 60 × 0.999 + (-9940 × 0.001) = 50
μₓ = $50
The variance, σₓ² = ∑[x² · P(x)] - μₓ²
Substituting gives;
The variance, σₓ² = 60² × 0.999 + ((-9940)² × 0.001) - 50² = 9990
The variance, σₓ² = 9990
The standard deviation, σₓ = √(σₓ²) = √(9990) ≈ 316.07
The standard deviation, σₓ ≈ $316.07
