An insurance policy costs $100 and will pay policyholders $10,000 if they suffer a major injury (resulting in hospitalization) or $3000 if they suffer a minor injury (resulting in lost time from work). The company estimates that each year 1 in every 2000 policyholders may have a major injury, and 1 in 500 a minor injury only. a) Create a probability model for the profit on a policy. b) What's the company 's expected profit on this policy? c) What's the standard deviation?

A) the probability model for the insurance company's profit:

x 100 - 9,900 - 2,900

P (X = x) 0.9975 0.0005 0.002

There is a 0.05% chance that there will be a major injury and a 0.2% chance of a minor injury, the chance of no injury happening is 99.75%.

B) the company's expected profit = ($100 x 0.9975) + (-$9,900 x 0.0005) + (-$2,900 x 0.002) = $99.75 - $4.95 - $5.80 = $89

C) the standard deviation is the square root of the variance, and the variance =

σ² = ∑ (x - μ) ² P (x) = (11² x 0.9975) + (9989² x 0.0005) + (2989² x 0.002) = 121 + 49,890 + 17,868 = 67,879

standard deviation = √σ² = √67,879 = 260.54