The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.

Payment ($)Probability00.825000.071,0000.043,0000.035,0000.028,0000.0110,0000.01(a)

Use the expected collision payment to determine the collision insurance premium (in dollars) that would enable the company to break even.

$

(b)

The insurance company charges an annual rate of $590for the collision coverage. What is the expected value of the collision policy (in dollars) for a policyholder? (Hint:It is the expected payments from the company minus the cost of coverage.) Why does the policy holder purchase a collision policy with this expected value?

expected value of the policy = $