Download Powerpoint on normal distribution

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript
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
•
•
•
•
•
•
•
•
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
•
•
•
•
% 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.
Related documents