Stat 101L: Lecture 8
Normal Models
Our conceptualization of what the
distribution of an entire population
of values would look like.
Characterized by population
parameters: μ and σ.
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30
Percent
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10
0
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45
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60
65
70
75
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Height
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Describe the sample
Shape is symmetric and mounded
in the middle.
Centered at 60 inches.
Spread between 45 and 75 inches.
30% of the sample is between 60
and 65 inches.
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1
Stat 101L: Lecture 8
Normal Models
Our conceptualization of what the
distribution of an entire population
of values would look like.
Characterized by a bell shaped curve
with population parameters
– Population mean = μ
– Population standard deviation = σ.
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Sample Data
0.08
0.07
Density
0.06
0.05
0.04
0.03
0.02
0.01
0.00
40
45
50
55
60
65
70
75
80
Height
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Normal Model
0.08
0.07
Density
0.06
0.05
σ
0.04
0.03
0.02
0.01
0.00
40
45
50
55
μ60
65
70
75
80
Height (inches)
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Stat 101L: Lecture 8
Normal Model
0.08
0.07
0.06
Sample – a
few items from
the population.
Example: 550
children.
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0.00
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45
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55
60
65
70
75
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Height (inches)
0.08
0.07
0.06
Density
Density
Population – all items
of interest.
Example: All children
age 5 to 19.
Variable: Height
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0.03
0.02
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0.00
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45
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Height
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Normal Model
Height
Center:
– Population mean, μ = 60 in.
Spread:
– Population standard deviation,
σ = 6 in.
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68-95-99.7 Rule
For Normal Models
– 68% of the values fall within 1
standard deviation of the mean.
– 95% of the values fall within 2
standard deviations of the mean.
– 99.7% of the values fall within 3
standard deviations of the mean.
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Stat 101L: Lecture 8
Normal Model - Height
68% of the values fall between
60 – 6 = 54 and 60 + 6 = 66.
95% of the values fall between
60 – 12 = 48 and 60 + 12 = 72.
99.7% of the values fall between
60 – 18 = 42 and 60 + 18 = 78.
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From Heights to Percentages
What percentage of heights fall
above 70 inches?
Draw a picture.
How far away from the mean is 70
in terms of number of standard
deviations?
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Normal Model
0.08
0.07
Density
0.06
0.05
0.04
Shaded
area?
0.03
0.02
0.01
0.00
40
45
50
55
60
65
70
75
80
Height (inches)
12
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