Transcript The Standard Normal Distribution

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 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.