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

Payment ($)	Probability
0	0.84
500	0.05
1,000	0.04
3,000	0.03
5,000	0.02
8,000	0.01
10,000	0.01

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

(b)The insurance company charges an annual premium of $585for 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.)