# Practical normal distribution problem

• Oct 8th 2013, 08:04 AM
Nora314
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!
• Oct 8th 2013, 09:54 AM
SlipEternal
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 $\displaystyle S_k$?