exercise:Af29700320: Difference between revisions
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Using the normal approximation, determine the smallest number of policies required in the portfolio that is divisible by 4 and large enough that the portfolio is profitable at least 95% of the time. | Using the normal approximation, determine the smallest number of policies required in the portfolio that is divisible by 4 and large enough that the portfolio is profitable at least 95% of the time. | ||
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<li>1,020</li> | <li>1,020</li> | ||
<li>1,032</li> | <li>1,032</li> | ||
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<li>1,680</li> | <li>1,680</li> | ||
<li>1,688</li> | <li>1,688</li> | ||
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Revision as of 13:48, 28 November 2024
A portfolio of annual policies are classified into two classes: class A and class B. You are given the following assumptions about the policies:
- Claim size is always 100 for class A policies and 200 for class B policies
- The probability of observing more than one claim per policy is zero for all policies in the portfolio
- The probability of observing a single claim in a year is 0.05 for class A policies and 0.03 for class B policies
- 25% of the policies in the portfolio belong to class A
- The expected loss for class A policies is 0.9 times the premium and the expected loss for class B policies is 0.8 times the premium.
Using the normal approximation, determine the smallest number of policies required in the portfolio that is divisible by 4 and large enough that the portfolio is profitable at least 95% of the time.
- 1,020
- 1,032
- 1,672
- 1,680
- 1,688