NormalDistribution - 3 - 14 -. 0 2 . 1. 8 3. 4 5 6. 6 8. 2...

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Unformatted text preview: 3 - 14 -. 0 2 . 1. 8 3. 4 5 6. 6 8. 2 9. 8 11. 4 13 Normal Distribution © 2004 Vertex42, LLC Wittwer, J. W., "Graphing a Normal Distribution in Excel" From Vertex42.com, November 1, 2004 http://vertex42.com/ExcelArticles/mc/NormalD Mean, µ Standard Deviation, σ Graph Limits zmin zmax ­4 4 10 2 Generate Random Normal NORMINV(rand(),mean,standard_dev) 6.2 Cumulative Probability xmin xmax Pr(x<xmin) Pr(x>xmax) Pr(xmin<x<xmax) Graphics 1 z= x− µ σ 8 11 15.87% 30.85% 53.28% 0.25 0.2 0.15 0.1 0.05 0 f ( x) = z ­4 ­3.8 ­3.6 ­3.4 ­3.2 ­3 ­2.8 ­2.6 ­2.4 ­2.2 ­2 ­1.8 ­1.6 ­1.4 ­1.2 ­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 2π σ 2 e − ( x− µ )2 2σ 2 0 0.25 0.2 2 4 6 8 10 12 14 16 18 20 0.25 0.2 Probability Density 0.15 0.1 0.05 0 0.6 0.4 0.2 0 2.8 2 4.4 5.2 6 7.6 6.8 9.2 10.8 12.4 10 14 15.6 17.2 18 3.6 8.4 11.6 13.2 14.8 16.4 Cumulative Probability x f(x) F(x) 2 0 0 2.4 0 0 2.8 0 0 3.2 0 0 3.6 0 0 4 0 0 4.4 0 0 4.8 0.01 0 5.2 0.01 0.01 5.6 0.02 0.01 6 0.03 0.02 6.4 0.04 0.04 6.8 0.06 0.05 7.2 0.07 0.08 7.6 0.1 0.12 8 0.12 0.16 8.4 0.14 0.21 8.8 0.17 0.27 9.2 0.18 0.34 9.6 0.2 0.42 10 0.2 0.5 10.4 0.2 0.58 10.8 0.18 0.66 Normal (Gaussian) Distribution 11.2 0.17 0.73 11.6 0.14 0.79 12 0.12 0.84 12.4 0.1 0.88 12.8 0.07 0.92 13.2 0.06 0.95 13.6 0.04 0.96 14 0.03 0.98 0.15 0.1 0.05 0 0 2 4 6 8 10 12 14 16 18 20 Cumulative Probability Graph 0.25 0.2 Probability Density 0.15 0.1 0.05 0 z x F(x) ­0.88 8.24 18.94% 39 18.94% 0 2 4 6 8 10 12 14 16 18 20 1 0.8 0.15 0.1 0.05 0 0.6 0.4 2.2 14.4 0.02 0.99 0.2 2.4 14.8 0.01 0.99 0 2.6 15.2 0.01 1 2.8 4.4 6 7.6 9.2 10.8 12.4 14 15.6 17.2 2.8 15.6 0 1 2 3.6 5.2 6.8 8.4 10 11.6 0 13.2 14.8 16.4 18 3 16 1 3.2 16.4 0 1 3.4 16.8 0 1 3.6 17.2 0 1 3.8 17.6 0 1 4 18 0 1 z ­4 0.25 0.2 0.15 0.1 0.05 0 0 2 4 x 2 2.15 2.3 2.45 2.6 2.75 2.9 3.05 3.2 3.35 3.5 3.65 3.8 6 3.95 4.1 4.25 4.4 4.55 4.7 4.85 5 5.15 5.3 5.45 5.6 5.75 5.9 6.05 6.2 6.35 6.5 6.65 6.8 6.95 7.1 7.25 7.4 7.55 7.7 f(x) 8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 12 14 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.06 0.06 0.07 0.08 0.09 0.09 0.1 F(x) 16 18 20 Cumulative Probability 0.2 Probability Density 1 0.8 7.85 8 z x 18 17.83 17.65 17.48 17.3 17.13 16.95 16.78 16.6 16.43 16.25 16.08 15.9 8 6 15.73 15.55 15.38 15.2 15.03 14.85 14.68 14.5 14.33 14.15 13.98 13.8 13.63 13.45 13.28 13.1 12.93 12.75 12.58 12.4 12.23 12.05 11.88 11.7 11.53 11.35 11.18 11 x 8 8.08 8.15 8.23 8.3 0.11 0.12 f(x) 4 0.25 0.2 0.15 0.1 0.05 0 0 2 4 10 0 0 0 0 0 0 0 0 0 0 0 0 0 12 14 0 0 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.03 0.03 0.04 0.05 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 16 18 20 z 0.25 0.2 0.15 0.1 0.05 0 0 2 4 f(x) 0.12 0.13 0.13 0.13 0.14 F(x) 6 8 10 12 14 16 18 20 0.25 0.2 0.15 0.1 0.05 0 0 2 4 8.38 8.45 8.53 8.6 8.68 8.75 8.83 8 6 8.9 8.98 9.05 9.12 9.2 9.27 9.35 9.42 9.5 9.57 9.65 9.72 9.8 9.87 9.95 10.03 10.1 10.18 10.25 10.33 10.4 10.48 10.55 10.63 10.7 10.78 10.85 10.93 11 10 0.14 0.15 0.15 0.16 0.16 0.16 12 0.17 14 0.17 0.17 0.18 0.18 0.18 0.19 0.19 0.19 0.19 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.19 0.19 0.19 0.19 0.19 0.18 0.18 0.18 16 18 20 z ­4 x 2 2.08 2.16 2.23 2.31 2.39 2.47 2.55 2.62 2.7 2.78 2.86 2.94 3.01 f(x) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.09 3.17 3.25 3.33 3.4 3.48 3.56 3.64 3.72 3.79 3.87 3.95 4.03 4.11 4.18 4.26 4.34 4.42 4.5 4.57 4.65 4.73 4.81 4.89 4.96 5.04 5.12 5.2 5.28 5.35 5.43 5.51 5.59 5.67 5.74 5.82 5.9 5.98 6.06 6.13 6.21 6.29 6.37 6.45 6.52 6.6 6.68 6.76 6.84 6.91 6.99 7.07 7.15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.06 0.06 0.06 0.07 0.07 7.23 7.3 7.38 7.46 7.54 7.62 7.69 7.77 7.85 7.93 8.01 8.08 8.16 8.24 0.08 0.08 0.08 0.09 0.09 0.1 0.1 0.11 0.11 0.12 0.12 0.13 0.13 0.14 2.com/ExcelArticles/mc/NormalDistribution­Excel.html 6 8 10 12 14 16 18 20 6 8 10 12 14 16 18 20 1 Cumulative Probability 0.8 0.6 0.4 .94% 0.2 0 10 12 14 16 18 20 ...
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This note was uploaded on 09/26/2009 for the course OM 550 taught by Professor Kin during the Spring '09 term at Universidad Católica del Maule.

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