According to the de Moivre–Laplace theorem, as n grows large, the shape of the discrete distribution converges to the continuous Gaussian curve of the normal distribution. The height of each dot is thus the probability of observing k heads when tossing n coins (a binomial distribution based on n trials). The possible number of heads on each toss, k, runs from 0 to n along the horizontal axis, while the vertical axis represents the relative frequency of occurrence of the outcome k heads. Consider tossing a set of n coins a very large number of times and counting the number of "heads" that result each time. Convergence in distribution of binomial to normal distribution Within a system whose bins are filled according to the binomial distribution (such as Galton's " bean machine", shown here), given a sufficient number of trials (here the rows of pins, each of which causes a dropped "bean" to fall toward the left or right), a shape representing the probability distribution of k successes in n trials (see bottom of Fig. 7) matches approximately the Gaussian distribution with mean np and variance np(1− p), assuming the trials are independent and successes occur with probability p.
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