Question

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

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

Payment (\$) Probability
0 0.82
500 0.05
1000 0.04
3000 0.04
5000 0.03
8000 0.01
10000 0.01

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

b. The insurance company charges an annual rate of \$595 for the collision coverage. What is the expected value of the collision policy for a policyholder? (Hint: It is the expected payments from the company minus the cost of coverage.) Enter negative values as negative numbers. Answer: \$

Why does the policyholder purchase a collision policy with this expected value?

The policyholder is concerned that an accident will result in a big repair bill if there is no Item 3 insurance coverage. So even though the policyholder has an expected annual loss of \$________ , the insurance - is protecting Item 5 against a large loss.