1. normal Distribution

2. Distribution Shapes

3. Normal Distribution Most common distribution in statistics
Many real-life data sets follow this pattern
Examples: SAT scores, heights of people, IQ tests
Also known as a bell curve

4. The Normal Distribution Curve
standard deviation
standard deviation
standard deviation
mean

5. 68% of the data falls within 2 standard deviations

6. 68% of the data falls within 4 standard deviations
95%

7. 68% of the data falls within 6 standard deviations
99.7%

8. When you break it up… (copy this!!)
34%
34%
.15%
.15%
13.5%
13.5%
2.35%
2.35%
mean
mean - 1SD
mean + 1SD
mean + 3SD
mean - 3SD
mean - 2SD
mean + 2SD

9. Example 1
Suppose that the average blood pressures of patients in a hospital follow a normal distribution with a mean of 108 and a standard deviation of 14. Set up a normal distribution curve.

10. Example 1
What percentage of patients have a blood pressure of 94 or higher?
What percentage of patients have a blood pressure between 80 and 122?
What percentage of patients have a blood pressure of less that 80?

11. Example 2
The duration of routine operations in a certain hospital has approximately a normal distribution with an average of 125 minutes and a standard deviation of 18 minutes. Set up a normal distribution curve.

12. Example 2
a) What percentage of operations last at least 125 minutes? b) What percentage of operations lasted between 107 and 143 minutes? c) What percentage of operations lasted between 89 and 125 minutes?

13. Example 3
The mean weight of 850 college students is 70 kg and the standard deviation of 3 kg. Set up a normal distribution curve.

14. Example 3 Determine how many of the 850 students weigh:
**This question is not asking for percents!
Between 64 kg and 73 kg.
More than 76 kg.
Less than 67 kg.
Between 70 kg and 76 kg.