# Thread: Standard Deviation and Empirical Rule

1. ## Standard Deviation and Empirical Rule

Say I have a bottle of beer that has mean weight of 500g with an SD of 25g. The QC decides to discard all the bottles that are more than 2SD lighter the mean weight, what percentage of the salt will be discarded, and what is the cut off value based on the empirical rule??

I know here that all bottles that are less than 450g will be discarded right, so that's the cut off value? Am I right?

2. Yes, it is 450.

$z=\frac{x-{\mu}}{\sigma}$

Now look that up in the z-table to get the percentage discarded.
The 68-95-99.7 Rule will get you close.

3. Originally Posted by galactus
Yes, it is 450.

$z=\frac{x-{\mu}}{\sigma}$

Now look that up in the z-table to get the percentage discarded.
The 68-95-99.7 Rule will get you close.
Yes understand that rule and removing the 2SD that means that 99.7-95 percent?? But this will also remove the 550 and above

4. The z-score is -2. Look that up in the table and we see it is .0228

Using the 95% rule for 2 standard deviations from the mean we would have .025. That's because 1-.95=.05. But that is for the other end also: .05/2=.025

5. Originally Posted by galactus
The z-score is -2. Look that up in the table and we see it is .0228