/sci/ - Science & Math

>>7366713
I actually made a mistake with the graph last time - bottom one wasn't stretched properly.

Anyways, when it comes to the normal distribution, the area under the curve from the left side to the cutoff (in this case, 120) is the way you calculate the percentage of people who are under that cutoff point, thus giving you the percentile score. The area under that curve is 1.000. The area from the left side to the cutoff is determined like this:

Subtract the given value (120) from the mean (100) and divide by the standard deviation (24). Then take that value (your z-score) and plug it in to this chart:

http://www.sixsigmastudyguide.com/wp-content/uploads/2014/04/z-table.jpg

Whatever you get is the percentile of that value on a normal distribution. Notice how a higher standard deviation reduces the z-score, thus lowering the percentile.