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An insurance company has a portfolio of 100 policyholders. 25 of the policyholders have loss distributions with mean 50 and variance 10, and 75 of

An insurance company has a portfolio of 100 policyholders. 25 of the policyholders have loss distributions with mean 50 and variance 10, and 75 of the policyholders have loss distributions with mean 10 and variance 30. Assuming the insurance company charges all policyholders the same premium, what premium should the company charge so that there is a 95% chance that aggregate claims will be less than the total premium collected?

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