An insurance company estimates that it should make an annual profit of $150 on each homeowners policy written, with a standard deviation of $6000. a) Why is the standard deviation so large

The standard deviation is so large because of the nature of the insurance business. In the vast majority of cases, the insurance company will have the profit of $150, that we can assume, is the price of the policy. However, in a few cases, the company will have losses that are very large, perhaps because of a house burning, or burglary, and those few large losses is what makes the standard deviation be so high.