Normal approximation to BinomialDe Moivre-Laplace limit theorem states that "for large n", the standard normal distribution approximates the binomial distribution (even though normal is continuous and binomial is discrete).Let's say you have a big box with many white and black balls in it. The black balls comprise 20% of the balls in the box.You can have a binomial trial started. Success is defined as a black ball drawn, and we know p=0.2 is the probability of success.Let's say the number of trials is 1000. That means the n is large. For each sample of 1000, count the number of black balls in the sample, and calculate the percentage of black balls in that sample. Let us say the first sample results in 28% black balls. On a horizontal axis, mark an X above a point that is marked .28.Return the balls to the box, mix them well, and take another sample of n=1000. Count the black balls in that sample, compute the percent of black balls, and plot it on the horizontal axis. Let us say it is 15%. Mark an X above the point that says 0.5 on the horizontal axis.
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