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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 |

- 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?

**a.**

To determine

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

**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,

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

x | f(x) | |

0 | 0 |

**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.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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