Normal Distribution.pdf

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Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 1
Chapter 6
The Normal
Distribution
Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 1

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 2
Chapter 6
The Normal Distribution

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 3
Section 6.1
Introducing Normally
Distributed Variables

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 4
Key Fact 6.1
Basic Properties of Density Curves
Property 1: A density curve is always on or above the
horizontal axis.
Property 2: The total area under a density curve (and
above the horizontal axis) equals 1.

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 5
Figure 6.1
Properties 1 and 2 of Key Fact 6.1

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 6
Key Fact 6.2
Variables and Their Density Curves
For a variable with a density curve, the percentage of all
possible observations of the variable that lie within any
specified range equals (at least approximately) the
corresponding area under the density curve, expressed
as a percentage.

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 7
Figure 6.2
Illustration of Key Fact 6.2

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 8
Definition 6.1
Normally Distributed Variable
A variable is said to be a normally distributed variable
or to have a normal distribution if its distribution has the
shape of a normal curve.

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 9
Table 6.1
Frequency and relative-frequency
distributions for heights

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 10
Figure 6.10 Relative-frequency histogram for
heights with superimposed normal curve

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 11
Key Fact 6.3
Normally Distributed Variables and Normal-Curve Areas
For a normally distributed variable, the percentage of all
possible observations that lie within any specified range
equals the corresponding area under its associated normal
curve, expressed as a percentage. This result holds
approximately for a variable that is approximately normally
distributed.

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 12
Definition 6.2
Standard Normal Distribution; Standard Normal Curve
A normally distributed variable having mean 0 and
standard deviation 1 is said to have the standard
normal distribution. Its associated normal curve is
called the standard normal curve, which is shown in
Fig. 6.11.
Figure 6.11

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 13
Key Fact 6.4

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 14
Figure 6.12
Standardizing normal distributions

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 15
Figure 6.13
Finding percentages for a normally distributed variable from
areas under the standard normal curve

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 16
Section 6.2
Areas Under the Standard
Normal Curve

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 17
Key Fact 6.5

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 18
Table 6.2
Areas under the standard normal curve

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 19
Figure 6.18
Using Table II to find the area under the standard normal
curve that lies (a) to the left of a specified z-score, (b) to
the right of a specified z-score, and (c) between two
specified z-scores
1.23
0.8907
-0.68 1.82
0.2483 0.9656

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 20
Definition 6.3

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 21
Figures 6.21 & 6.22
Finding z 0.025
Finding z 0.05
Z 0.0344 = -1.82
Zα

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 22
Section 6.3
Working with Normally
Distributed Variables

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 23
Procedure 6.1

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 24
Figure 6.25
Determination of the percentage of people having IQs
between 115 and 140
x=115 x=140
Z1= 115-100/16= 0.94 = 0.8264
Z2= 140-100/16= 2.50 = 0.9938
0.9938-0.8264= 0.1674 16.74%

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 25
Key Fact 6.6

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 26
Figure 6.26
-3 -2 -1 0 1 2 3

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 27
Procedure 6.2

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 28
Section 6.4
Assessing Normality; Normal
Probability Plots

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 29
Key Fact 6.7

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 30
Table 6.5
Ordered data and
normal scores

Copyright © 2017 Pearson Education, Ltd. Chapter 6, Slide 31
Figure 6.29
Normal probability plot for the sample of adjusted gross
incomes

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