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

Payment ($) ....................... Probability
0 ................................................. .85
500 ............................................. .04
1000 .......................................... .04
3000 .......................................... .03
5000 .......................................... .02
8000 .......................................... .01
10000 ........................................ .01

a. Use the expected collision payment to determine the collision insurance premium that would enable the company to break even.

b. The insurance company charges an annual rate of $520 for the collision coverage. What is the expected value of the collision policy for a policyholder? Why does the policyholder purchase a collision policy with this expected value?