Calculating z distribution formula?

Question

I have a dataset, and z values for these. I want to calculate their probability percentage (z distribution), but not using the table (i.e. http://www.isixsigma.com/library/content/zdistribution.asp) I want to calculate it by hand since this is for a computer program. What is that formula?

Answer 1

im so sorry i forgot the formula. but i know something where you might get help since i had my stat last sem. try to download the free software R-language and some tutorials about this can be found in the net.

Answer 2

1. You can use excel program to find z , =NORMSDIST(VALUE).
2. You can curvefit the values from table to get approximate formula.
3. From http://en.wikipedia.org/wiki/Normal_distribution#Standardizing_normal_random_variables. the formula is
Pr(X<=x) = (1/2)(1+erf[(x-mu)/[sigma(sqrt of 2)]
mu is the mean
sigma is the standard deviation.
Also u can use excel for error function (erf) , as add-on in excel (engineering functions). or still a table.
So it is better to curvefit the table. (http://www.oakdaleengr.com/) - Datafit

Answer 3

Im not quite sure what you're asking but here is the standard Z formula from which you can decipher X, SD and the mean.
Z=(X-mean)/sd

Answer 4

∞
∫[(1/(σ√2π))e^- ((1/2)((x - μ)/σ)^2) = Z
-∞
Define z = (x - μ)/σ. Then
∞
∫[(1/(σ√2π))e^- ((1/2)z^2) = Z
-∞
Integrate numerically, choosing ∆z as small or large as you wish (smaller gives better precision). For most applications, starting at z = - 5 using 0.01 steps will yield adequate results.