Central Limit Theorem

Central Limit Theorem and probability distributions
Discrete random variables ...

The central limit theorem basically states that as the sample size (N) becomes large, the following occur:
The sampling distribution of the mean becomes approximately normal regardless of the distribution of the original variable.

Moreover, without going into details regarding the derivation of this formula, we also know (because of the central limit theorem, and thus approximate normal distribution of the means; see, for example, Hoyer and Ellis, 1996) that the distribution ...

Vice versa a large variety of instances may be quickly solved in an approximate way via the central limit theorem in terms of confidence interval around a Gaussian distribution - that's the benefit.

Parametric Bootstrap
Central Limit Theorem
Non parametric boostrap
Eric Weiss explain how to perform Bootstrap in SAS
Bootstrap in MS Excel (without macro free download) ...

By the central limit theorem, this method will display $1/\backslash sqrt\{N\}$ convergence-\; i.e.\; quadrupling\; the\; number\; of\; sampled\; points\; will\; halve\; the\; error,\; regardless\; of\; the\; number\; of\; dimensions.$$

See also: Distribution, Normal distribution, Variance, T distribution, Demon