# Exam P Practice Problem 29 – Expected Insurance Payment

Problem 29A

When there is a loss due to fire damage to a house, the loss follows the distribution indicated below.

$\displaystyle \begin{bmatrix} \text{Loss Amount}&\text{ }&\text{Probability} \\\text{ }&\text{ }&\text{ } \\ 5,000&\text{ }&0.5 \\ 10,000&\text{ }&0.3 \\ 50,000&\text{ }&0.1 \\ 75,000&\text{ }&0.05 \\ 100,000&\text{ }&0.03 \\ 150,000&\text{ }&0.015 \\ 200,000&\text{ }&0.005 \end{bmatrix}$

The owner of the house purchases an insurance policy with a deductible of 5,000 to insure againse this loss. What is the expected payment to the owner under this policy.

$A. \ \ \ \ \ \text{15,000}$
$B. \ \ \ \ \ \text{15,500}$
$C. \ \ \ \ \ \text{20,500}$
$D. \ \ \ \ \ \text{31,000}$
$E. \ \ \ \ \ \text{30,000}$

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Problem 29B
Use the same information as in Problem 29A. What is the standard deviation of the payment to the owner under this insurance policy?

$A. \ \ \ \ \ \text{29,541.49}$
$B. \ \ \ \ \ \text{30450.18}$
$C. \ \ \ \ \ \text{31,480.15}$
$D. \ \ \ \ \ \text{35,597.34}$
$E. \ \ \ \ \ \text{38,749.19}$

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