The total amount for a health insurance policy follows a distribution with density function
$f(x) =\dfrac{1}{1000}e^{-x/1000},for~x0$
The premium for the policy is set at 100 over the expected total claim amount. If 100 policies are sold, whet is the approximate probability that the insurance company will have claims exceeding the premiums collected?
Please, help

Question

The total amount for a health insurance policy follows a distribution with density function 
$f(x) =\dfrac{1}{1000}e^{-x/1000},for~x>0$
The premium for the policy is set at 100 over the expected total claim amount. If 100 policies are sold, whet is the approximate probability that the insurance company will have claims exceeding the premiums collected?
Please, help

loser66 · Answer

@Zarkon 
I don't know understand this sentence "The premium for the policy is set at 100 over the expected total claim amount"
Is it not that the expected total claim amount is E(x) = 1000? , then we need find P(X>1100)?