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The Normal Distribution: Comparing Apples and Oranges f ( x) e 1 / 2 ( x 2 )2 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 CurveStandard 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. • Normal Probability Plot – a plot of the observed values of the variable being considered versus the normal scores.