Normal Approximation of Binomial Distribution - Maple Help

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Normal Approximation of the Binomial Distribution

 Main Concept The binomial distribution is a discrete probability distribution that is used to obtain the probability of observing exactly k number of successes in a sequence of n trials, with the probability of success for all single trials of p.   The shape of the binomial distribution is dependent on the values of n and p, as illustrated in the following diagrams: The normal distribution is a continuous probability distribution whose shape is dependent on the mean, m, and variance, σ.   Since a binomial variate, B(n,p), is a sum of n independent, identically distributed Bernoulli variables with parameter p, it follows that by the central limit theorem it can be approximated by the normal distribution with mean  and variance , provided that both  and .

In the following example, adjust the binomial probability mass function by moving the sliders for the values of n and p. The red line shows the probability density function for the normal distribution.

n:

p:

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