What is the history behind normal distribution?

Answer 1

The discovery of the Normal distribution is sometimes attributed to de Moivre, who in 1738 published his results on the coefficients in the binomial expansion of (a + b)n. He calculated results for the mean and spread of the binomial expansion. Although it is now possible to relate his theorem to the Normal approximation of the Binomial Distribution, de Moivre himself, was unable to do so because he was unaware of the the concept of a probability density function.

In 1809, while developing the theory concerning the method of least squares he concluded that the only law which worked was to use the normal law of errors.

A year later Marquis de Laplace proved the Central Limit Theorem. According to this, no matter what the underlying density functions, the means of repeated samples from a population tended towards a nomal distribution. It was also he who calculated the integral of exp(-t2)dt as being sqrt(pi) which allowed the function to be normalised.