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Question

# 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. a) Why is the standard deviation so large? b) If it writes only two of these policies, what are the mean and standard deviation of the annual profit? c) If it writes 10,000 of these policies, what are the mean and standard deviation of the annual profit? d) Is the company likely to be profitable? Explain. e) What assumptions underlie your analysis? Can you think of circumstances under which those assumptions might be violated? Explain.

Solution

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(a)

Profit of $150$ on each homeowner's policy written will be a lot of gains and the insurance company do not have to give to most but will pay out a huge amount of money to some and that causes to have a huge losses. That is why the standard deviation is so large.

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