Normal Approximation to Binomial Distribution Consider the binomial distribution with n trials, and probability of success is p This distribution is approximately normal if np > 5 and nq > 5. In this case it is approximated by a normal distribution with Mean = np and Variance = npq Consider the binomial distribution with n trials, and probability of success is p This distribution is approximately normal if np > 5 and nq > 5. In this case it is approximated by a normal distribution with Mean = np and Variance = npq

This binomial distribution doesn’t look approximately normal (it is not bell shaped). Note np = > 5 but nq = 1.25 < 5.

The normal distribution is a good approximation: np = (25)(.7) = 17.5 > 5, nq = (25)(.3) = 7.5 > 5

The normal is a good approximation: np = 32> 5 and nq = 8 > 5.

The normal is a good approximation: np = 40> 5 and nq = 60 > 5.

Ex: For the following distribution, estimate P(9 < r < 13) by (i)using the binomial probability formula directly; (ii)using the normal approximation.

Continuity Correction

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