Stat 101L: Lecture 9
Standardizing
z=
z=
y−μ
σ
70 − 60
= 1.67
6
1
Standard Normal Model
Table Z: Areas under the standard
Normal curve in the back of your
text.
On line:
http://davidmlane.com/hyperstat/z_table.html
2
From Percentages to Heights
What height corresponds to the
75th percentile?
Draw a picture.
The 75th percentile is how many
standard deviations away from the
mean?
3
1
Stat 101L: Lecture 9
Normal Model
0.08
25%
0.07
Density
0.06
0.05
50%
0.04
25%
0.03
0.02
0.01
0.00
40
45
50
55
60
65
70
75
80
Height (inches)
4
Standard Normal Model
Table Z: Areas under the standard
Normal curve in the back of your
text.
On line:
http://davidmlane.com/hyperstat/z_table.html
5
Reverse Standardizing
z=
y−μ
σ
y − 60
6
y = (6 * 0.67 ) + 60 = 64.02
0.67 =
6
2
Stat 101L: Lecture 9
Do Data Come from a
Normal Model?
The histogram should be mounded in
the middle and symmetric.
The data plotted on a normal
probability (quantile) plot should
follow a diagonal line.
– The normal quantile plot is an option in
JMP: Analyze – Distribution.
7
Do Data Come from a
Normal Model?
Octane ratings – 40 gallons of
gasoline taken from randomly selected
gas stations.
Amplifier gain – the amount
(decibels) an amplifier increases the
signal.
Height – 550 children age 5 to 19.
3
.99
2
.95
.90
1
.75
0
.50
.25
Normal Quantile Plot
8
-1
.10
.05
-2
.01
-3
6
4
Count
8
2
85
90
Octane Rating
95
9
3
Stat 101L: Lecture 9
Normal Quantile Plot
3
.99
2
.95
.90
1
.75
0
.50
.25
-1
.10
.05
-2
.01
-3
25
15
Count
20
10
5
7.5
8
8.5
9
9.5
10 10.5 11 11.5 12
Amplifier Gain (dB)
10
.95
.90
.75
.50
.25
.10
.05
.01
Normal Quantile Plot
3
.99
2
1
0
-1
-2
-3
Count
150
100
50
45
50
55
60
65
Height
70
75
11
Nearly normal?
Is the histogram basically
symmetric and mounded in the
middle?
Do the points on the Normal
Quantile plot fall close to the red
diagonal (Normal model) line?
12
4