Lecture 9 The Normal Distribution

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The Normal Distribution

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Lecture 9 The Normal Distribution BA 201 Lecture 9 The Normal Distribution © 2001 Prentice-Hall, Inc.

Topics The Normal Distribution The Standardized Normal Distribution © 2001 Prentice-Hall, Inc.

Continuous Probability Distributions Continuous Random Variable Values from interval of numbers Absence of gaps Continuous Probability Distribution Distribution of continuous random variable Most Important Continuous Probability Distribution The normal distribution © 2001 Prentice-Hall, Inc.

The Normal Distribution p.199 The Normal Distribution “Bell Shaped” Symmetrical Mean, Median and Mode are Equal Interquartile Range Equals 1.33 s Random Variable has Infinite Range f(X) X  Mean Median Mode © 2001 Prentice-Hall, Inc.

The Mathematical Model (Called the Probability Density Function) © 2001 Prentice-Hall, Inc.

Many Normal Distributions p.201 Many Normal Distributions There are an Infinite Number of Normal Distributions Varying the Parameters X and X, We Obtain Different Normal Distributions © 2001 Prentice-Hall, Inc.

The Standardized Normal Distribution p.201 The Standardized Normal Distribution Given , has a standardized (normalized) normal distribution where f(Z) f(X) X © 2001 Prentice-Hall, Inc.

Finding Probabilities pp.203-212 Finding Probabilities Probability is the area under the curve! f(X) X a b c d © 2001 Prentice-Hall, Inc.

Standardized Normal Distribution pp.203-212 Example: Standardized Normal Distribution Normal Distribution Shaded Area Exaggerated © 2001 Prentice-Hall, Inc.

pp.203-212 Example: (continued) Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 .02 .5832 0.0 .5000 .5040 .5080 Shaded Area Exaggerated 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 Z = 0.21 0.3 .6179 .6217 .6255 © 2001 Prentice-Hall, Inc.

pp.203-212 Example: (continued) Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 .02 .4168 -0.3 .3821 .3783 .3745 Shaded Area Exaggerated -0.2 .4207 .4168 .4129 -0.1 .4602 .4562 .4522 Z = -0.21 0.0 .5000 .4960 .4920 © 2001 Prentice-Hall, Inc.

Normal Distribution in PHStat PHStat | Probability & Prob. Distributions | Normal … Example in Excel Spreadsheet © 2001 Prentice-Hall, Inc.

Summary Discussed the Normal Distribution Described the Standard Normal Distribution © 2001 Prentice-Hall, Inc.