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Normal Distribution
and The Empirical
Rule
Get out your notes.
Open Note Unit 3 Test on
Friday.
Learning Objectives
• Be able to recognize a normal distribution
curve
• Be able to use the Empirical Rule to
predict measurements that are normally
distributed.
• Apply the Empirical Rule to predicting the
quality of measured blocks.
Probability Distribution
Distribution
A distribution of all possible values of a variable
with an indication of the likelihood that each will
occur
– A probability distribution can be represented by
a probability density function
• Normal Distribution – most commonly used probability
distribution
http://en.wikipedia.org/wiki/File:Normal_Distribution_PDF.svg
Normal Distribution Quick
Check
“Is the data distribution normal?”
1.Translation: Is the
histogram/dot plot bell-shaped?
2.Does the greatest frequency of the
data values occur at about the mean
value?
3.Does the curve decrease on both
sides away from the mean?
4.Is the curve symmetric about the
mean?
Noteworthy
Normal Distribution?
Distribution
Frequency
Bell shaped
curve
6
5
4
3
2
1
0
1
2
Data Elements
3
4
5
6
Normal Distribution?
Distribution
Does the greatest frequency of the
data values occur at about the
mean value?
Frequency
Mean Value
6
5
4
3
2
1
0
1
2
Data Elements
3
4
5
6
Normal Distribution ?
Distribution
Does the curve decrease
on both sides away from
the mean?
Frequency
Mean Value
6
5
4
3
2
1
0
1
2
Data Elements
3
4
5
6
Normal Distribution?
Is the curve symmetric
about the mean?
Frequency
Mean Value
6
5
4
3
2
1
0
1
2
Data Elements
3
4
5
6
What if the data is not symmetric?
Histogram Interpretation: Skewed (Non-Normal) Right
What if the data is not symmetric?
A normal distribution is a reasonable assumption.
Review
1. How can you determine if it is a Normal
Distribution?
2. Bell Shaped Curve
3. Peaks at the mean
4. Curve decreases on both sides away from the
mean
5. Curve is symmetric. Looks the same on both
side.
Learning Objectives
• Be able to recognize a normal distribution
curve
• Be able to use the Empirical Rule to
predict measurements that are normally
distributed.
• Apply the Empirical Rule to predicting the
quality of measured blocks.
Empirical Rule
• Applies to normal distributions
• Almost all data will fall within three
standard deviations of the mean
Empirical Rule
If the data are
normally
distributed:
• 68% of the observations fall within 1 standard deviation
of the mean.
• 95% of the observations fall within 2 standard deviations
of the mean.
• 99.7% of the observations fall within 3 standard deviations
of the mean.
Empirical Rule Example
Data from a
sample of a
larger
population
0.08 + 1.77
= 1.88
0.08 + - 1.77
= -1.69
Normal Distribution
68 %
s
s
-1.77 +1.77
Data Elements
0.08 + 3.54
= 3.62
0.08 + -3.54
= - 3.46
Normal Distribution
95 %
2s
- 3.54
2s
+ 3.54
Data Elements
Your Turn
Revisit the data you collected during the
Fling Machine Instant Challenge.
• Assume that you repeated launch cotton
balls with your device. Using the mean and
sample standard deviation of your data:
– Predict the range of travel distances within
which 68% of cotton balls would fall
– Predict the range of travel distances within
which 95% of cotton balls would fall
Example
Example
Review
• What is the Empirical Rule?
• Given a mean value of 10 with a standard
deviation of 2:
– What range of values would 68% of the data
fall in?
– What range of values would 95% of the data
fall in?
– What range of values would 99.7% of the data
fall in?
• Can you apply the Empirical rule to all sets
of data?
Tasks
Friday’s Test is Open Notes (Your notebooks), not
internet/cell phone/Smith’s Website
• Complete Worksheet 3.3 (the cube measuring
worksheet)
• When finished you can check past PowerPoints and add
information to your notes to be used on Friday’s exam.
• Test Topics
– US/SI Measurements
– Unit Conversions
– Using Dial Calipers
– Statistics: Mean, Median, Mode, Standard Deviation,
Histogram
– Using Excel to calculate statistics
– Normal Curves
– The Empirical Rule