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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? ( Hint: It is the expected payments from the company minus the cost of coverage.) Why does the policyholder purchase a collision policy with this expected value?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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Chapter
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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 5.3, Problem 20E
Textbook Problem
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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
  1. a. Use the expected collision payment to determine the collision insurance premium that would enable the company to break even.
  2. 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? (Hint: It is the expected payments from the company minus the cost of coverage.) Why does the policyholder purchase a collision policy with this expected value?

a.

To determine

Find the collision insurance premium that would enable the company to break even using the expected collision payment.

Explanation of Solution

Calculation:

The data represents the probability distribution for the damage claims paid by an insurance company on collision insurance.

The formula for the expected value of a discrete random variable is,

E(x)=μ=xf(x)

The expected value of the insurance claim is obtained using the following table:

xf(x)xf(x)
00

b.

To determine

Find the expected value of the collision policy for a policy holder and to explain why the policyholder does purchase a collision policy with this expected value.

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