Download mean

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.
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.
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
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
• Practice Test