An Insurance Company Estimates That It Should Make an Annual

Multiple Choice

An insurance company estimates that it should make an annual profit of $150 on each homeowner's policy written,with a standard deviation of $6000.If it writes three of these policies,the mean annual profit for the company is found to be 3 × 150 = 450.The standard deviation of the company's annual profit is found to be
≈ $10,392.What assumptions (if any) underlie the calculation of the mean? of the standard deviation?

A) Mean: that the profit on each policy follows a Normal model
Standard deviation: that the policies are independent of one another and that the profit on each policy follows a Normal model
B) Mean: no assumptions required
Standard deviation: no assumptions required
C) Mean: no assumptions required
Standard deviation: that the policies are independent of one another and that the profit on each policy follows a Normal model
D) Mean: no assumptions required
Standard deviation: that the policies are independent of one another
E) Mean: that the policies are independent of one another
Standard deviation: that the policies are independent of one another