In fact, the insurance company sees that in the entire population of homeowners, the mean loss from fire is μ = $300 and the standard deviation of the loss is σ = $400. what are the mean and standard deviation of the average loss for 10 policies? (losses on separate policies are independent. round your standard deviation to two decimal places.)

If we based solving this using the Central Limit Theorem, then if are given n random variables (in this case, losses from fire) and all with mean μ and standard deviation σ, then the distribution of the average of these random variables will behave in a normal distribution with mean μ and standard deviation σ / sqrt (n). Therefore the rules are:

μ’ = μ

σ’ = σ / sqrt (n)

So if we are given 10 policies, n = 10. Therefore the new mean μ’ and standard deviation σ’ are:

μ’ = $300

σ’ = $400 / sqrt (10) = $126.49