# 12.4 The Normal Distribution - homepages.ohiodominican.edu

```Thinking
Mathematically
Statistics:
12.4 The Normal Distribution
Remember mean and standard
deviation?
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 21/2 standard deviations above the
mean.
The 68-95-99.7 Rule for the Normal Distribution
99.7%
95%
68%
-3
-2
-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.
Examples: The 68%, 95%, 99.7%
Rule
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.
Computing z-Scores
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?
Thinking
Mathematically
Statistics:
12.4 The Normal Distribution
```
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