Normal Distribution - places to look for it

Question

If i were to look around for items, objects or any 'samples' for that matter, which ones would give me a normal distribution?

I know heights and weights of people could give me a normal distribution. Scores of a test in class of certain number of students could give me a normal distribution. However, i want to look at things other than those already known to give a normal distribution.

What other places could i look for it?

Answer 1

Some ideas:

• Travel time from A to B
• Working hours of a lightbulb
• Weight of apples
• Volume of potatoes

Answer 2

Nearly no example fits the bill (especially not the ones mentioned in the post) if one considers some raw data. Nearly every example does if one considers some suitably renormalized data.

In other words, when observing, say, the heights $H(x)$ of some actual people, then obviously no $H(x)$ is normally distributed (since for example no height is negative). But the renormalized heights $$h_n=\frac1{\sqrt{n}}\sum\limits_x(H(x)-m),$$ based on a sample of size $n$, will often be approximately normally distributed, provided at least three conditions hold:

• The size $n$ of the sample is large
• The raw data $H(x)$ are translated by a suitable quantity $m$
• The sample is not built up from several populations with different (statistical) properties

Note that to give meaning to, and, possibly, quantify these properties is no trivial matter.