Hello,



More of my philosophy about the central limit theorem and about my
PERT++ and more..

I am a white arab, and i think i am smart since i have also
invented many scalable algorithms and algorithms..


The central limit theorem states that the sampling distribution of the
mean of any independent, random variable will be normal or nearly
normal, if the sample size is large enough.

How large is "large enough"?

In practice, some statisticians say that a sample size of 30 is large
enough when the population distribution is roughly bell-shaped. Others recommend a sample size of at least 40. But if the original population
is distinctly not normal (e.g., is badly skewed, has multiple peaks,
and/or has outliers), researchers like the sample size to be even
larger. So i invite you to read my following thoughts about my software
project that is called PERT++, and notice that the PERT networks are
referred to by some researchers as "probabilistic activity networks"
(PAN) because the duration of some or all of the arcs are independent
random variables with known probability distribution functions, and have
finite ranges. So PERT uses the central limit theorem (CLT) to find the expected project duration.

And as you are noticing this Central Limit Theorem is also so important
for quality control, read the following to notice it(I also understood Statistical Process Control (SPC)):

An Introduction to Statistical Process Control (SPC)

https://www.engineering.com/AdvancedManufacturing/ArticleID/19494/An-Introduction-to-Statistical-Process-Control-SPC.aspx

Also PERT networks are referred to by some researchers as "probabilistic activity networks" (PAN) because the duration of some or all of the arcs
are independent random variables with known probability distribution
functions, and have finite ranges. So PERT uses the central limit
theorem (CLT) to find the expected project duration.

So, i have designed and implemented my PERT++ that that is important for quality, please read about it and download it from my website here:

https://sites.google.com/site/scalable68/pert-an-enhanced-edition-of-the-program-or-project-evaluation-and-review-technique-that-includes-statistical-pert-in-delphi-and-freepascal

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So I have provided you in my PERT++ with the following functions:


function NormalDistA (const Mean, StdDev, AVal, BVal: Extended): Single;

function NormalDistP (const Mean, StdDev, AVal: Extended): Single;

function InvNormalDist(const Mean, StdDev, PVal: Extended; const Less: Boolean): Extended;

For NormalDistA() or NormalDistP(), you pass the best estimate of
completion time to Mean, and you pass the critical path standard
deviation to StdDev, and you will get the probability of the value Aval
or the probability between the values of Aval and Bval.

For InvNormalDist(), you pass the best estimate of completion time to
Mean, and you pass the critical path standard deviation to StdDev, and
you will get the length of the critical path of the probability PVal,
and when Less is TRUE, you will obtain a cumulative distribution.


So as you are noticing from my above thoughts that since PERT networks
are referred to by some researchers as "probabilistic activity networks"
(PAN) b