An insurance company charges $1000 for a one-year policy for an automobile that is valued at $30,000. The company's actuaries have determined that all accidents fall into one of three categories: 1 in 500 policyholders will be involved in an accident that causes a loss of one-third of the value of the car at some time during the year, 1 in 800 policyholders will be in an accident that causes a loss of two-thirds of the value of the car, and 1 in 1250 will incur a total loss of their vehicle's value.

In case of an accident, the policyholder will owe the insurance company a $1000 deductible, and the insurance company will owe the policyholder for the dollar value of his or her loss in each case.

Let X represent the profit of the insurance company per one-year policy. Copy and paste the table below and fill in the cells for the probability distribution of X.

X
P(X)

Calculate the expected profit per one-year policy for the insurance company.

Compute the standard deviation of X= profit of the insurance company per one-year policy.

Interpret the expected value you calculated above in Question 2.

If the insurance company sold 10 policies, how much would they expect to profit?