Download presentation

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

Similar presentations

Presentation is loading. Please wait....

OK

AP Statistics Section 2.1 B

AP Statistics Section 2.1 B

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on oxidation and reduction for class 10 Ppt on indian textile industries in ethiopia Ppt on conservation of species Ppt on conservation of natural resources Ppt on outside activities for preschoolers Ibm si view ppt online Ppt on combination of resistances organization Ppt on statistics in maths what is the factor Free ppt on brain machine interface Best way to show ppt on ipad