The Normal Distribution:Comparing Apples and Oranges

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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.