Section 2.2, Part 2
Determining Normality
AP Statistics
What is “Normal”?

Because we should only apply z-score to
distributions that are normal, we need a
process to determine whether a
distribution is a normal distribution.
AP Statistics, Section 2.2, Part 2
2
Symmetric?
The distribution should be roughly
symmetric.
 You can use a Boxplot to determine
symmetry.

AP Statistics, Section 2.2, Part 2
3
Are Walter Johnson’s Wins
Normal?



5, 14, 13, 25, 25, 33,
36, 28, 27, 25, 23, 23,
20, 8, 17, 15, 17, 23,
20, 15, 5 into list L1
Run “1-Var Stats”
Is the data set
symmetric? Where do
you look?
AP Statistics, Section 2.2, Part 2
4
Are Walter Johnson’s Wins
Normal?


Look also at boxplot
Is the data set
symmetric?
AP Statistics, Section 2.2, Part 2
5
68-95-99.7 Rule?

You can use the 68-95-99.7 rule with a
histogram to see if the distribution roughly
fits the rule.
AP Statistics, Section 2.2, Part 2
6
Are Walter Johnson’s Wins
Normal?

5, 5, 8, 13, 14, 15, 15, 17,
17, 20, 20, 23, 23, 23, 25,
25, 25, 27, 28, 33, 36
AP Statistics, Section 2.2, Part 2
7
Are Walter Johnson’s Wins
Normal?


Last step is the creation of the “normal
probability plots
Let’s look at the book example:
AP Statistics, Section 2.2, Part 2
8
Example 2.12
X
Midpoint
Y
1
1/8=.1250
-1.15
2
3/8=.3750
-.319
2
5/8=.6250
.319
3
7/8=.8750
1.15
AP Statistics, Section 2.2, Part 2
9
Example 2.12
X
Midpoint
Y
1
1/8=.1250
-1.15
2
3/8=.3750
-.319
2
5/8=.6250
.319
3
7/8=.8750
1.15
AP Statistics, Section 2.2, Part 2
10
Example 2.12
X
Midpoint
Y
1
1/8=.1250
-1.15
2
3/8=.3750
-.319
2
5/8=.6250
.319
3
7/8=.8750
1.15
AP Statistics, Section 2.2, Part 2
11
Somewhat normal
(somewhat linear)
AP Statistics, Section 2.2, Part 2
12
Example 2.12
X
Midpoint
Y
1
1/10=.1
-1.282
2
3/10=.3
-0.524
2
5/10=.5
0.000
3
7/10=.7
0.524
10
9/10=.9
1.282
AP Statistics, Section 2.2, Part 2
13
Example 2.12
X
Midpoint
Y
1
1/10=.1
-1.282
2
3/10=.3
-0.524
2
5/10=.5
0.000
3
7/10=.7
0.524
10
9/10=.9
1.282
AP Statistics, Section 2.2, Part 2
14
Example 2.12
X
Midpoint
Y
1
1/10=.1
-1.282
2
3/10=.3
-0.524
2
5/10=.5
0.000
3
7/10=.7
0.524
10
9/10=.9
1.282
AP Statistics, Section 2.2, Part 2
15
Not normal (not linear)
AP Statistics, Section 2.2, Part 2
16
Walter Johnston Normal?
AP Statistics, Section 2.2, Part 2
17
Assignment
Exercises 2.26 – 2.31, 2.33, 2.36 to finish
Section 2.2
 Exercises 2.39, 2.40, 2.42, 2.45, 2.47 to
finish Chapter 2

AP Statistics, Section 2.2, Part 2
18