The Normal distribution
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![Page 1: The Normal distribution](https://reader030.fdocuments.us/reader030/viewer/2022033106/56813300550346895d99bf0a/html5/thumbnails/1.jpg)
and the 68-95-99.7 Rule
THE NORMAL DISTRIBUTION
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SKEWED DISTRIBUTIONS & OUTLIERS
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NORMAL = TYPICAL• This is valuable information when studying
human behavior • i.e., the average woman is 5’4” tall (64 inches) …
this means that we expect to see women of this height. It is uncommon to see women who are 6 feet tall or 4 feet tall.
• i.e., the average intelligence score is 100…it is rare to score 130 or 70.
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• Standard Deviation
• Range
• Mean
• Median
• Mode
DESCRIBING ‘NORMAL’ W/ STATSCENTRAL TENDENCY VARIATION
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IN ORDER TO INTERPRET THE NORMAL CURVE BOTH PIECES OF INFORMATION ARE NECESSARY.
WHY?
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• Did everyone get a 30?
• Did half of the students get a 20 and the other half get a 40?
• Was my score good or bad?
I.E., THE AVERAGE SCORE ON THE QUIZ WAS 50 POINTS…
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• We know how spread out the grades are but not how they are centered
• How did the class do in general?
• Is my grade good or bad?
I.E., THE SD ON THE QUIZ WAS 5
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• Allows us to make accurate assumptions and inferences about data on a normal curve
68-95-99.7 RULE
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68% OF ALL DATA WILL FALL WITHIN ONE STANDARD DEVIATION OF THE MEAN.
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95% OF ALL DATA WILL FALL WITHIN TWO STANDARD DEVIATIONS OF THE MEAN.
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99.7% OF ALL DATA WILL FALL WITHIN THREE STANDARD DEVIATIONS OF THE MEAN.
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QUIZ EXAMPLE…M=50 AND SD=5• Now we know that 68% of students scored between 45
and 55
• 95% of students scored between 40 and 60
• 99.7% of students scored between 35 and 65
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Height example…M=64, SD=3So…68% of all women are within 3 inches of 64.68% of all women are within 1 standard deviation of the mean.
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95% of all women are within 2 standard deviations of the mean.Here 95% of all women are within 6 inches of 64.
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99.7% of all women are within 3 standard deviations of the mean.Here 99.7% of all women are within 9 in. of 64.
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PRACTICE PROBLEMS
• The average height at TCC is 66 inches with a standard deviation of 4.5 inches. Display this information on a normal curve.
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• How tall is someone 2 standard deviations above the mean?
• Answer: 66+4.5+4.5=75 inches • What percentage of students are between
61.5 and 70.5 inches?• Answer: 68%
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• What percentage of students are below 70.5?
• Answer: 84%• 50%+34%=84%
• What percentage of students are below 75?
• Answer: 97.5
• What percentage of students are above 79.5?
• Answer: 0.15%