A company offers a renters insurance policy that costs a customer $60 per year, and the company will make a payout of $10,000 to the customer if they are victim to theft in that year. The company set this price based on the probability of a theft in the area being 0.001. The table below displays the probability distribution of x = the company's profit from one of these policies.

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

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