# Normal distribution

1. Nov 13, 2009

### disregardthat

What properties does some measurement possess such that they fit along a normal curve? And how was the general formula found? Wikipedia says very little on this.

2. Nov 13, 2009

### mathman

The normal distribution comes out of one of the fundamental theorems in probability theory "Central Limit Theorem". The general idea is that when adding up, and properly normalizing, a large number of independent random variables, the distribution of the result is approximately normal.

3. Nov 13, 2009

### disregardthat

What assumptions are we making about the nature of our measurements when we assume they will fit the normal curve?

4. Nov 14, 2009

### mathman

The errors are random in nature, independent from each other. If there is a systematic error, it will show up as an error in the mean (assuming you have a theoretical mean to compare).

5. Nov 14, 2009

### disregardthat

Could you describe it in another way? I am aware of the "errors" from the mean in nature, but what is characteristic for the distribution of these error which makes the normal curve an appropriate model?

The distribution curve for a binomial experiment fits the normal curve. Are we in some sense assuming that the measurements have the same characteristics? If so, in what sense?

6. Nov 15, 2009

### mathman

The main point is that the errors be independent. The binomial approaches the normal because the assumptions of the central limit theorem hold.

7. Nov 15, 2009

### disregardthat

How does the independence of errors imply that it is normally distributed?

8. Nov 16, 2009

### mathman

I suggest that you look up the central limit theorem. If you google "Central Limit Theorem Proof" you will get a wealth of information.