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

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

$$1$

b$.$ The insurance company charges an annual rate of $$580$ 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.

$

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

insurance coverage. So even though the policyholder has an expected annual

loss of $

$,$ the insurance

against a large loss.