Why do many phenomenon follow the Normal law distribution in nature ?

Why do many phenomenon follow the Normal law distribution in nature ?

I would intuitively expect the distribution in red to be more prevalent.

How do you explain the green phenomenon ?

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Central limit theorem

Not intuitive.

I'm asking about an explanation as to why it goes against intuition and you answer a meme ?

Because the world doesn't have harsh cutoffs like in red. Normal has the rapid decline to infinity which makes it more "realistic"

>I would intuitively expect the distribution in red to be more prevalent.

Why? How is a sharp edged triangle with no limits the slightest bit intuitive?

CLT deals with sampling, which is not what OP is asking about

>why doesn't the world have harsh cutoffs ?

because the world doesn't have harsh cutoffs

flawless talmudic bongo player logic

because the distribution has to be finite, symmetric and peak at the middle

>because the distribution has to be finite
Yes but the limits don't have to be, and it would seems intuitive to me that there would be inifinite limits.

Fundamentally the reason the normal distribution pops up so much is because it's a simple byproduct of the way we statistically analyze data. It appears because it 'has' to whenever we measure 'continuous' properties (height etc). There's always the 'data clump' in the middle that causes the 'unbalance' in the shape because nature tends to the average, usually because there are more paths to reach it than there are to the extremes. It's hard to describe without a specific example though desu.

probability density distribution

youtube.com/watch?v=X2eomv6XfWo

it stems from repeated binary events that have some constant error involved and are repeated to infinity. the classic example is the plinko board, pic related, when you drop a ball into the middle slot, slot 5 here. the ball will go left or right after hitting the peg, go to the next peg and go left or right, go to the next peg...

if we had a very large number of pegs and dropped a bunch of balls the resulting distribution would be normal.

what said is truth, not a meme. you flip 100 coins, 1 is heads, 0 is tails, and sum up the flips. now repeat these trials to infinity. resulting distribution is normal. why? well you're just playing a plinko game with 100 pegs.

bump

idealized binary situations are completely intuitive

real life situations are completely UNintuitive

what want is an explnation of why are most probability distributions in nature the same as a 50-50 binary peg distribution ?

and no, central limit therem is a nonintuitive hand wavy explanation, thus a meme

for example the CLT doesn't explain why the bottom green arrows are longer than the top ones

2/2

how do you explain intuitively that the inflexion points of the normal distribution are at -1 and +1 ?

>what want is an explnation of why are most probability distributions in nature the same as a 50-50 binary peg distribution ?
most aren't, not without transforming the data first.
if you disagree with this and can explain why, then you'll have found your answer.

>how do you explain intuitively that the inflexion points of the normal distribution are at -1 and +1 ?
first you must explain intuitively what an inflexion point is and why anyone should care

>How do you explain the green phenomenon

because there's always something more interesting happening in the middle, and the graph itself is self-aware and trying to crunch itself into the middle

Just look at a proof of the central limit theorem.
It will become intuitive when you see why it is true - there's nothing hand-wavy about giving a precise, mathematical answer to your question, quite the opposite.
The central limit theorem applies to all distributions (that have a well defined mean), which is why it applies in nature.

What are you saying? What's the green phenomenon?

the fucking universe is self-aware and actively trying to prevent improbable shit from happening

there is no such thing as a universe

wots all this then

What's the equation of that graph? Looks awesome

i don't actually know
some user posted it here and never told anyone the equation

>central limit theorem
>not intuitive
brainlet or just too lazy to actually read the proof?

Yes, but in nature, we sample anyway to get the data. CLT states that any sufficiently large sample of x, as seen in populations in nature, xbar will have a normal distribution.

Google normal distribution function

Sure, for any given statistic [math]\overline{x}[/math], the summary value approximates a normal distribution, but that still says nothing about the underlying distribution.

You can sample from an exponential distribution and get a sample mean with a normal distribution, but that doesn't mean the underlying distribution is normal.

you are dumb.

courses.ncssm.edu/math/Talks/PDFS/normal.pdf

This gives a nice derivation of the normal distribution function. If the nature of some process can be described by the assumptions made in the derivation, then it can be described by a bell curve.

not OP but thanks user