Question

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.)

Answer 1

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