The Normal Distribution Comparing Apples and Oranges Topics
The Normal Distribution: Comparing Apples and Oranges Topics: • Essentials • Normal Curves • Standard Normal • Non-Standard to Standard • z-score • Empirical Rule • Assessing normality
Essentials: Normal Distribution (I’m normal. . . or am I? ) • Be able to identify normal and approximately normal distributions. • Know the characteristics of the Standard Normal. • Be able to use the Standard Normal table. • Empirical Rule and the Standard Normal. • Transforming Non-Standard distributions to the Standard Normal.
Three Normal Distributions
Frequency and Relative Frequency Distributions for Heights
Relative Frequency Histogram for a Normally Distributed Variable
The Standard Normal Curve
Properties of the Standard Normal Curve • 1. The Standard Normal Distribution has a mean of 0 and a standard deviation of 1. • 2. The total area under the curve is equal to 1. • 3. The Standard Normal Curve extends indefinitely in both directions, approaching, but never touching the horizontal axis. • 4. The Standard Normal Curve is symmetric about 0; that is, the part of the curve to the left of 0 is a mirror image of the part of the curve to the right of it. • 5. Most of the area under the curve lies between -3 and 3 (99. 74%).
Normal Curve Standard Normal Curve
Standardizing Normal Distributions
The Empirical Rule Revisited
Assessing Normality • Pearson’s Index of Skewness (I) – The closer to a value of zero, the less skewed, or more normal, the data set. Recall that if I lies between -1 and +1 the distribution is considered to be approximately normally distributed. .
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