Revision 06. Normal Approximation to Binomial

# Revision 06. Normal Approximation to Binomial - Normal...

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Normal Approximation to the Binomial (n=30, p=0.2) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 The binomial distribution has mean, μ = np = 6, and variance σ 2 = npq =4.8 If we draw a Normal distribution curve with the same mean and variance, there is a close correspondence between the two.

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For the Binomial distribution, P(X=6) = area of the green block on the diagram This can be approximated by the Normal probability P(5.5<X<6.5) where X has mean 6, and variance 4.8. “Continuity correction” Normal Approximation to the Binomial (n=30, p=0.2) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Normal Approximation to the Binomial (n=30, p=0.2) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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Revision 06. Normal Approximation to Binomial - Normal...

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