There are N Poi(100) i. claims, each distributed as an X Exp(1). The total amount of losses S is the sum of these claims.

There are N ∼ Poi(100) i.i.d. claims, each distributed as an X ∼ Exp(1). The total amount of losses S is the sum of these claims. Using the normal approximation, find the value at risk for the confidence level 99%, that is, the amount