Normal Approximation to a Binomial Random Variable

parameter n

20

parameter p

0.5

compute agreement

A binomial random variable with parameters

n

and

p

can be thought of as a sum of independent Bernoulli random variables, each with parameter

p

. The central limit theorem implies that for large values of

n

a binomial random variable can be well approximated by a normal random variable with the same mean and variance. A measure of agreement between the two is obtained by computing the purple area; 100% represents complete agreement between the two distributions. The computation of the purple area is slow, so use the sliders with the "compute agreement" box unchecked.