# Central limit theorem

1. Sep 27, 2010

### rhyno89

1. The problem statement, all variables and given/known data

The cross sectional area of a tube is u = 12.5 and SD = .2. When the area is less than 12 or greater than 13 it wont work. They are shipped in boxes of 1000, determine how many per box will be defective

2. Relevant equations

3. The attempt at a solution

So I think I have the solution but am a little confused with the process. To start I normalized the variables into Z values. So I did (12-12.5)/.2 and (13-12.5)/.2. When it was all said and done I found it to equal .0124 x 1000 = aprx 12 defects.

My question is do I have to add any correction factor while normalizing like for the binomial approximation and do I have to change the mean. I know that some types of these problems require me to start by multiplying the mean by the number and doing a similar change to the standard deviation. I don't really need much help with the computation, just getting a little confused with all the different cases.

Thanks alot

2. Sep 27, 2010