Central limit theorem right|thumb|250px|As the number of discrete events increases, the function begins to resemble a normal distribution. thumb|250px|Comparison of probability density functions, for the sum of fair 6-sided dice to show their convergence to a normal distribution with increasing , in accordance to the central limit theorem. In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve).
central limit theorem right|thumb|250px|as the number of discrete events increases the function begins to resemble a normal distribution thumb|250px|comparison of probability density functions for the sum of fair 6-sided dice to show their convergence to a normal distribution with increasing  in accordance to the central limit theorem in the bottom-right graph smoothed profiles of the previous graphs are rescaled superimposed and compared with a normal distribution (black curve)