Download Powerpoint on normal distribution

Normal distribution
An example from class
Histogram for Female Ability to Match
Stick Angle
8
7
5
4
3
2
1
19
17
15
13
11
9
7
5
3
0
1
Frequency
6
Classes of number of sticks correctly
matched
Example Of a Normal Variable
HEIGHTS OF MOTHERS
CLASS LIMITS(in.)
FREQUENCY
52-53
53-54
54-55
55-56
56-57
57-58
58-59
59-60
60-61
61-62
62-63
63-64
64-65
65-66
66-67
67-68
68-69
69-70
70-71
0.5
1.5
1
2
6.5
18
34.5
79.5
135.5
163
183
163
114.5
78.5
41
16
7.5
4.5
2
1052
TOTAL
Histogram Of Heights Of Mothers (in.)
Frequency
200
150
100
50
0
Height
Normal distribution
Bell-shaped curve
0.08
Mean = 70 SD = 5
0.07
Density
0.06
0.05
0.04
Mean = 70 SD = 10
0.03
0.02
0.01
0.00
40
50
60
70
Grades
80
90
100
Characteristics of
normal distribution
• Symmetric, bell-shaped curve.
• Shape of curve depends on population mean ()
and standard deviation ().
• Center of distribution is mean () and mode and
median.
• Spread is determined by standard deviation().
• Most values fall around the mean, but some values
are smaller and some are larger.
Examples of normal
random variables
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testosterone level of male students
head circumference of adult females
length of middle finger of Stat/Soc students
Height
Weight
IQ scores
Body temperature
Repeated measurement of same quantity
Probability between 65 and 70?
0.08
0.07
Density
0.06
0.05
P(65 < X < 70)
0.04
0.03
0.02
0.01
0.00
55
60
65
70
Grades
75
80
85
Probability above 75?
Probability student scores higher than 75?
0.08
0.07
Density
0.06
0.05
P(X > 75)
0.04
0.03
0.02
0.01
0.00
55
60
65
70
Grades
75
80
85
Probability below 65?
0.08
0.07
Density
0.06
0.05
0.04
0.03
0.02
P(X < 65)
0.01
0.00
55
65
75
Grades
85
Normal Percents
The 68-95-99.7 Rule
Example: Young Women’s Height
• The heights of young women are approximately normal
with mean = 64.5 inches and std.dev. = 2.5 inches.
Example: Young Women’s Height
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% of young women between 62 and 67?
% of young women lower than 62 or taller than 67?
% between 59.5 and 62?
% taller than 68.25?
Example: Young Women’s Height
• The heights of young women are
approximately normal with mean = 64.5
inches and std.dev. = 2.5 inches.
Example: Young Women’s Height
• The heights of young women are approximately normal
with mean = 64.5 inches and std.dev. = 2.5 inches.
Example: Young Women’s Height
•
•
•
•
% of young women between 62 and 67?
% of young women lower than 62 or taller than 67?
% between 59.5 and 62?
% taller than 68.25?
Working With the General Normal
EXAMPLE: IQ Scores
IQ Scores have a normal distribution with a mean of 100 and
a standard deviation of 16. What is the 99% percentile of IQ
Scores?
s.d. = 16
|
100
The Standard Normal Table: Table A
• Table A is a table of areas under the standard normal density
curve. The table entry for each value z is the area under the
curve to the left of z.