Practical normal distribution problem

Hi!

My problem:

A machine at a factory performs a procedure to make a chemical. A poisonous by-product

is formed in an amount of X grams every time the machine performs the procedure, where

X has the normal distribution with mean 20 and standard deviation 4. If more than 25 g

of the by-product is formed, a warning lamp lights up and stays lit until the procedure is

nished. The machine can be set so that it performs the procedure multiple times, but it

cannot be stopped until all is finished. The amount of by-product is independent each time

the procedure is performed.

d) The pollution authorities require that the probability that the machine produces 500 g

or more by-product in one day, should be 0.01 or less. How many times can the machine

perform the procedure during of one day for this requirement to be satised?

I managed to solve, a , b , and c, but I am completely stuck on this one. The right answer should be 0,100, any help would be really appreciated, thanks!

Re: Practical normal distribution problem

Suppose the machine performs its task k times. Let $\displaystyle X_i$ be the amount of by-product produced on the $\displaystyle i$-th process. Let $\displaystyle S_k = \sum_{i=1}^k X_i$. It is easy to check that the expected value for $\displaystyle S_k$ is $\displaystyle 20k$. How would you determine the standard deviation for $\displaystyle S_k$?