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Normal approximation to Binomial
De MoivreLaplace 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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This note was uploaded on 11/13/2011 for the course MBA 522 taught by Professor Nabavi during the Spring '08 term at Bellevue.
 Spring '08
 Nabavi

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