An Insurance Company Estimates That It Should Make an Annual $3 \times 150 = 450$

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 $3 \times 150 = 450$ The standard deviation of the company's annual profit is found to be $\sqrt { 6000 ^ { 2 } + 6000 ^ { 2 } + 6000 ^ { 2 } } \approx \$ 10,392 .$ 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