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Chapter 9 – The Normal
Distribution
Math 22
Introductory Statistics
Properties of the Normal
Distribution
Basic properties of all normal distributions:
 The total area under the curve is equal to 1
 The distribution is bell shaped and symmetric
 The curve extends to infinity in both directions
 The distribution is centered at the mean
 The mean is equal to the median
Properties of the Normal
Distribution
 The
area under the curve between any
two points of the normal distribution is
equal to the probability of observing a
value between those two points.
z - Score
 Number
of standard deviations an
observation resides from the mean.
observatio n - mean
z
standard deviation
x  x
z
x
The Standard Normal
Distribution
 The
mean is equal to 0.
 The standard deviation is equal to 1.
Finding Probabilities
probabilities using the TI – 83.
 Percentiles
 Finding