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An insurance company estimates that it should make an annual profit of ​$230 on each​ homeowner's policy​ written, with a standard deviation of ​$5000 .

Why is the standard deviation so​ large?

a. 

There will be many gains of ​$230 with a few large losses. 

b. If the company writes only two of these​ policies, what are the mean and standard deviation of the annual​ profit?

Mean = 2 * $230 =  $460. 

Standard deviation = square root (5000^2 * 2) = ?

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c) If the company writes​ 10,000 of these​ policies, what are the mean and standard deviation of the annual​ profit?

standard deviation = sqrt(5000^2 * 10000) = 500000

mean =  $2300000

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