# Thread: Practical normal distribution problem

1. ## 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 satis ed?

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!

2. ## Re: Practical normal distribution problem

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