1. Ch 2 – The Normal Distribution YMS – 2.1
Density Curves and
the Normal Distributions

2. Vocabulary Mathematical Model Density Curve
An idealized description of a distribution
Density Curve
Is always on or above the horizontal axis
Has area = 1 underneath it
Can roughly locate the mean, median and quartiles, but not standard deviation
Mean is “balance” point while median is “equal areas” point.

3. Reminder: Exploring Data on a Single Quantitative Variable
Always plot your data
Identify socs
Calculate a numerical summary to briefly describe center and spread
Describe overall shape with a smooth curve
Label any outliers

4. Next 2 classes – Fathom Activity and Sketching WS
Greek Notation
Population mean is μ and population standard deviation is σ
These are for idealized distributions (population vs. sample)
Classwork p83 #2.1 to 2.5
Next 2 classes – Fathom Activity and Sketching WS

5. Activity: Beauty and the Geek More Vocabulary
Normal Curves
Are symmetric, single-peaked and bell-shaped
They describe normal distributions
Inflection point
Point where change of curvature takes place
Could use this to estimate standard deviation

6. 3 Reasons for Using Normal Distributions
1. They are good descriptions for some distributions of real data.
2. They are good approximations to the results of many kinds of chance outcomes.
3. Many statistical inference procedures based on normal distributions work well for other roughly symmetric distributions.

7. The Rule
In N(μ, σ), rule gives percent of data that falls within 1, 2, and 3 standard deviations, respectively.
AKA Empirical Rule
Classwork p89 #
Homework p90 #2.12, 2.14, 2.18
and 2.2 Reading Blueprint

8. Sketch a bell curve for each of the following:
p(x < a ) = 0.5
p(x > b) = 0.5
p(x < c) = 0.8
p(x < d) = 0.2
p(x > e) = 0.05
p(x > f) = .95

9. Standard Normal Calculations
YMS – 2.2
Standard Normal Calculations

10. Standards Standard Normal Distribution
Standardized value of x (z-score)
Data point minus mean divided by standard deviation
Gives you the number of standard deviations the data point is from the mean

11. Table A Left Column has ones.tenths digit
Top Row has 0.0hundreths digit
LEFT COLUMN + TOP ROW = Z-SCORE
Area is always to the LEFT of the z-score

12. TI-83 Plus Keystrokes 2nd DISTR 1: normalpdf
Finds height of density curve at designated point
We won’t be using this
2: normalcdf(lower limit, upper limit, mean, st. dev.)
Gives area under the curve to left or right of a point
3:invNorm(area, mean, standard deviation)
*When you don’t enter a mean or standard deviation, it assumes it is the Normal Distribution (0, 1)

13. In Class Exercises p95 #2.19-2.20 Homework p103 #2.21-2.25

14. Activity: Grading Curves WS Normal Probability Plots (NPP)
Is a plot of z-scores vs. data values
Use the calculator!
If it’s a straight line, the data is normally distributed.
How else do we assess normality?

15. In Class Exercises (Next 3 days) Shape of Distributions WS p108 #2
In Class Exercises (Next 3 days) Shape of Distributions WS p108 #2.27 p113 # , , , AP Practice Packet