Does the distribution follow the 68-95-99.7% rule?

Normal density curves satisfy the following property which is often referred to as the Empirical Rule.  Almost all values lie within 3 standard deviations of the mean for a normal distribution.

68% of the observations fall within 1 standard deviation of the mean.
95% of the observations fall within 2 standard deviations of the mean.
99.7% of the observations fall within 3 standard deviations of the mean.

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Also, in a normal distribution, the mean, median, and mode are equal so that is a quick test of normality.

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Look at step two from:

http://www.netgm.com/tools/useful_stuff/process_capability.html

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Remember, large sample theory says basically that the larger the sample size, the closer one approaches a normal distribution. See: http://www.stat.sfu.ca/~lockhart/richard/450/99_3/lectures/13/web.html

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More links on normal distributions:

http://ce597n.www.ecn.purdue.edu/CE597N/1997F/students/michael.a.kropinski.1/project/tutorial
http://www.stat.wvu.edu/SRS/Modules/Normal/normal.html
http://davidmlane.com/hyperstat/normal_distribution.html
http://mathworld.wolfram.com/NormalDistributionFunction.html
http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661

Thank you Leanne for your help.  Your feedback will definitely help me immensely.  Take care.

Leanne,
On the first link you gave me it shows five steps to calculate process capability.  I am confused about one thing though.  My data showed that it was non-normal so I went ahead and transformed it by grouping the data n=109 samples into 3 groups, took the average, and calculated the Z value of the transformed data and of course the transformed Z plot was a straight line since averages always have a normal dist. In order to calculate my process capability now do I have to calculate the USL and LSL, X-bar, and std. dev. using just the 3 averaged data points or the 3 transformed Z values in order to come up with Cp and Cpk? or did I transform it just to graph which it wouldn't make sense cause I still need my Cp calculation. Please advise the website is not clear.  Thanks.

calpoly, let me see what I can dig up. Most of my stat books are about 1200 miles away. I'm not sure what I have here & it's been a long time since I did any CpK/Cp calculations (I only have so much RAM these days - if I don't use a technique daily, I have to look it up.)

Do you have any SPC books? I have the Pyzdek book somewhere, but I'm not sure if it's with me here or in Texas. I'm going to be offline tomorrow - have to drive up to Chi-town to pick up DS' "new" car so it may be a few days.

In the meantime if you have a time crunch, don't wait on me, hit a library and see what you can find on SPC.

calpoly, there is a programm you may be know, it's called Arena, you have to give in the data in a matrix, WordPad or Excel, and than when you do the Imput Analyzer, in Arena,  and than the Fit All solution it tells you which is the right distribution, it show you also the grafic.

AxelCS