Question

How large a number makes a normal distribution? With an explanation.

Answer 1

The normal distribution is useful because of the central limit theorem. In its most general form, under some conditions, it states that average of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal, that is become normally distributed when the no.of observations is sufficiently large.

Physical quantities that are expected to be the sum of many independent procesess often have distributions that are nearly normal. Moreover, many results and methods(such as propagation of uncertainty and least squares parameter fitting) can be derived anlytically in explicit form when the relavent variables are normally distributed. The normal distribution is sometimes informally called the bell shaped curve. However many other distribution are bell shaped.