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Section 6.1
Introduction to the Normal
Distribution
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Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
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All rights reserved.
Objectives
o Identify the properties of a normal distribution.
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Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.
Properties of a Normal Distribution
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4.
Properties of a Normal Distribution
A normal distribution is bell-shaped and symmetric
about its mean.
A normal distribution is completely defined by its
mean, m, and standard deviation, s.
The total area under a normal distribution curve
equals 1.
The x-axis is a horizontal asymptote for a normal
distribution curve.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.
The Standard Normal Distribution
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Properties of the Standard Normal Distribution
The standard normal distribution is bell-shaped and
symmetric about its mean.
The standard normal distribution is completely
defined by its mean, m = 0, and standard deviation,
s = 1.
The total area under the standard normal
distribution curve equals 1.
The x-axis is a horizontal asymptote for the standard
normal distribution curve.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.
Example 6.1: Calculating and Graphing z-Values
Given a normal distribution with μ = 48 and s = 5,
convert an x-value of 45 to a z-value and indicate where
this z-value would be on the standard normal
distribution.
Solution
Begin by finding the z-score for x = 45 as follows.
x  m 45  48
z

 0.60
s
5
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Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.
Example 6.1: Calculating and Graphing z-Values
(cont.)
Now draw each of the distributions, marking a standard
score of z = −0.60 on the standard normal distribution.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.
Example 6.1: Calculating and Graphing z-Values
(cont.)
The distribution on the left is a normal distribution with
a mean of 48 and a standard deviation of 5. The
distribution on the right is a standard normal
distribution with a standard score of z = −0.60
indicated.
HAWKES LEARNING SYSTEMS
Students Matter. Success Counts.
Copyright © 2013 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.