I also pulled back a similar posting for a similar reason.
Ah, you’re right! First time for everything, heh? j/k
I’ve just always done it that way because....I don’t know why? Easier to keep it together in my head, I guess. Speaking of z-scores and whatnot, I figured out how to do the formula on wolframalpha and keep a bookmark to it on my phone. Change the (0.25) to whatever z-score you want.
https://www.wolframalpha.com/input/?...%5E2)%2F2)++du
Unless there’s an easier (but still accurate/precise?) formula?
"Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]
Unfortunately there is no simpler formula because the Gaussian normal distribution function cannot be analytically integrated because of the -u^2 square in the exponential function. Many functions can be analytically integrated by another function given as a short formula (the so-called anti-derivative function from Calculus), but not the Gaussian one.
So you need large tables with function values or a computer in order to approximately compute the integral (= area under the curve), e.g. by the Simpson integration rule, which requires about 10 to 100 iteration steps in a loop to get sufficient precision in the results, depending on the desired number of precise digits.
Last edited by PinkChip; 07-21-2019 at 05:39 AM.
"Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]
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