Question

A company offers a flood insurance policy that costs a homeowner $200 per year, and the company will make a payout of $100,000 to the homeowner if they have a flood in that year. The company set this price based on the probability of a flood in the area being 0.001. The table below displays the probability distribution of X=X= the company's profit from one of these policies.

No flood Flood
X=profit $200 -$99,800
P(X) 0.999 0.001

Given that μX​=$100, calculate σX​.
You may round your answer to the nearest dollar.

Answer 1

σX​ = 3161

Explanation:

The standard deviation is the square root of the multiplication of each probability multiplied by the squared difference between the values and the mean.

In this question:

`\sigma X = √(0.999*(200-100)^2 + 0.001*(-99800-100)^2) = 3160.7`

Rounding to the nearest dollar, σX​ = 3161