Normal approximation

[TrueTears]

Saw this in a question somewhere... not sure what it meant so I did some research. I understand that it's an approximation for binomial distribution when the sample group is very large, so it's approximated to be the same as a normal distribution. but is there a formal prove of how this is so?

[Mao]

Saw this in a question somewhere... not sure what it meant so I did some research. I understand that it's an approximation for binomial distribution when the sample group is very large, so it's approximated to be the same as a normal distribution. but is there a formal prove of how this is so?

This is akin to asking for a formal proof of linear regression.

When dealing with statistics and things of that like, try not to be too accurate

[EvangelionZeta]

Saw this in a question somewhere... not sure what it meant so I did some research. I understand that it's an approximation for binomial distribution when the sample group is very large, so it's approximated to be the same as a normal distribution. but is there a formal prove of how this is so?

This is akin to asking for a formal proof of linear regression.

When dealing with statistics and things of that like, try not to be too accurate

...wut?? o_o

[TrueTears]

Saw this in a question somewhere... not sure what it meant so I did some research. I understand that it's an approximation for binomial distribution when the sample group is very large, so it's approximated to be the same as a normal distribution. but is there a formal prove of how this is so?

This is akin to asking for a formal proof of linear regression.

When dealing with statistics and things of that like, try not to be too accurate

lol, alright, thanks for that Mao.

[kamil9876]

I think it's a fair question to ask. Even the study of approximations like is still about precision, because you can precisely show that the approximation can be as good as you want it to be i.e for any for some large enough .

I guess his question is really akin to "what is normal distribution, is the definition of it at all tied to binomial? maybe do another argument to see if it is at all related to binomial?"

To be honest I don't know what the answer to that question is because statistics just sounds so boring and I've paid no attention to it at all. Maybe it will satisfy a bit of curiosity though




edit: I guess I just have a vague notion that any continous probability really just comes from discrete probability (u know, that histogram diagram, or that fun breaking the stick into three pieces question (from SUPER-HAPPY-FUN-MATHS time, didn't even use calculus there and just took the limit of a discrete case). It would seem very unnatural that some random function would fit something so natural like binomial, so it was probably made from the binomial, a bit of google found this:

"de Moivre developed the normal distribution as an approximation to the binomial distribution,"

http://mathworld.wolfram.com/NormalDistribution.html