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Normal Distribution
Name____________________________
12-3
Data can be "distributed" (spread out) in different ways. There are many cases where the data tends to be around
a central value with no bias left or right, and it gets close to a "Normal Distribution" like this:
Many things closely follow a Normal Distribution: heights of people, size of things produced by machines,
errors in measurements, blood pressure, marks on a test.
We say the data is "normally distributed".
The Normal Distribution has:



mean = median = mode
symmetry about the center
50% of values less than the mean
and 50% greater than the mean
The Standard Deviation is a measure of how spread out numbers are.When you calculate the standard deviation
of your data, you will find that:
68% of values are within
1 standard deviation of the
mean
95% are within 2 standard
deviations
99.7% are within 3 standard
deviations
Example #1: How are the heights of professional athletes distributed?
The frequency table below lists the heights of the 2001 Baltimore Ravens. The table shows the heights of the
players, but it does not show how these heights compare to the heights of an average player. To make that
comparison, you can determine how the heights are distributed.
Height (in.)
Frequency
67
1
69
1
70
4
71
4
72
10
73
6
74
6
75
8
76
7
77
5
80
1
a) Determine the mean, median and standard deviation. Round to the nearest tenth.
b) Are the heights normally distributed? Justify your answer.
 Approximately what percent of the heights fall within one standard deviation of the mean?

Approximately what percent should it be to be considered normally distributed?

Approximately what percent of the heights fall within two standard deviations of the mean?

Approximately what percent should it be to be considered normally distributed?
c) Can we conclude that the data is normally distributed?
Example #2: Are the weights of Red Alaskan King Crabs normally distributed?
Biologists are studying the weights of Red King Crabs in the Alaskan waters. They sample 16 crabs and
compiled their weights, in pounds, as shown below.
9.8
10.1
11.1
12.4
11.8
13.2
12.8
12.5
13.7
11.6
13.4
12.3
12.6
14.8
14.2
a) Determine the mean, median and standard deviation. Round to the nearest tenth.
b) Are the weights normally distributed? Justify your answer.
 Approximately what percent of the weights fall within one standard deviation of the mean?

Approximately what percent should it be to be considered normally distributed?

Approximately what percent of the weights fall within two standard deviations of the mean?

Approximately what percent should it be to be considered normally distributed?
c) Can we conclude that the data is normally distributed?
15.1