12.4 The Normal Distribution

Exercise Set 12.4 #5
A set of test scores are normally distributed with a mean of 100 and a standard deviation of 20. Find the score that is 2 1 /
2 mean.
standard deviations above the

The 68-95-99.7 Rule for the Normal Distribution
99.7%
95%
68%
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3
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2
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1
1 2 3

The 68-95-99.7 Rule for the Normal Distribution
1.
Approximately 68% of the measurements will fall within 1 standard deviation of the mean.
2.
Approximately 95% of the measurements will fall within 2 standard deviations of the mean.
3.
Approximately 99.7% (essentially all) the measurements will fall within 3 standard deviations of the mean.

Exercise Set 12.4 #15, #25
The mean price paid for a particular model of car is
$17,000 and the standard deviation is $500 (see graph in text). Find the percentage of buyers who paid between $16,000 and $17,000.
IQs are normally distributed with a mean of 100 and a standard deviation of 16. Find the percentage of scores between 68 and 100.

A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. The z-score can be obtained using z-score = data item – mean standard deviation
Data items above the mean have positive z - scores. Data items below the mean have negative z-scores. The z-score for the mean is 0.
Exercise Set 12.4 #35
A set of data items is normally distributed with a mean of 60 and a standard deviation of 8. What is the z score for 84?

12.4 The Normal Distribution