1. Chapter 2: The Normal Distributions
Density Curves
Normal Distribution
Standard Distribution

2. Density Curve Mathematical model for a distribution
Always on or above the horizontal axis
Has an area of exactly 1
There are normal, skewed left, and skewed right curves
To find a value, find the area under the curve
Quartile 1=1/4 of the area under the curve
Quartile 3=3/4 of the area under the curve

3. Median and Mean of Density Curves
Median—equal-areas point: divides the area under the curve in half
Mean—the balance point: where the curve would balance if made solid
Symbol:
Mean and median are equal on a symmetric curve

4. Normal Curve

5. Skewed Right Curve

6. Skewed Left Curve

7. Normal Curve
Must be:
Symmetric
mean=median
Single Mound
Bell Shaped

8. Normal Distribution Mean Standard Deviation
Can be written—N(mean, standard deviation)
Changing the Standard Deviation changes the spread of the curve
Changing the mean without changing the standard deviation moves the graph horizontally on the x-axis
Larger Standard Deviation=curve more spread out
Inflection Point-points where the curvature change takes place
Located a from each side of the mean

9. The 68-95-99.7 Rule 68% of all observations fall within of
To find an observation’s percentile, use the Z-Score

10. Graph of Rule

11. Example
The distribution of heights of adult American men is approximately normal with mean of 69 inches and a standard deviation of 2.5 inches. Between what heights do the middle 68% of men fall?
69+2.5=71.5
69-2.5=66.5
From 66.5 to 71.5

12. Z-Score To find what percentage a certain individual/value is
Tells us how many standard deviation we are from the mean
Formula-
Can use the table or the calculator
Calculator
normalcdf(lower bound, upper bound, mean, standard deviation)

13. Z-Score Table

14. Assessing Normality Method 1—Frequency Histogram or Stem Plot
Approximately bell-shaped
Symmetric about the mean
Check to see if rule works
Method 2--Normal Probability Plot
Interpret the graph—if the plotted points appear to be close to a line, then it is a normal distribution

15. The End