Dedução da equação da curva normal

Resumo

This paper deals with the mathematical basis of the normal frequency distribution. The author derives the analytical expression of the normal distribution function by the method developed by Gauss to determine the error function, instead of using the binomial approximation.

The arbitrary constants that come out are determined through the conditons the function ought to fulfill. The final result is expressed in terms ol the population parameters, ie., the mean 4 and the variance o². The theoretical basis underlying the elaboration of the table of the area under the normal curve is explained in detail.

To make the article more accessible to persons not well acquainted with advanced calculus technique it is avoided as much as possible to skip the intermediate steps.