The Normal Distribution: Comparing Apples and Oranges

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 The total area under the curve is equal to 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. Normal Probability Plot – a plot of the observed values of the variable being considered versus the normal scores.