1. Probability the likelihood of specific events

2. Probability
We are going to focus on three types of probability problems
Normal Curve Probabilities
Binomial situations
Simple combined event probabilities

3. The Normal Curve The Natural Law of Errors
Properties of the Normal Distribution
Percentile Ranks based on the Normal Distribution

4. The Natural Law of Errors
Many things in nature are distributed normally
Heights and weights, as well as other physical features of many living things
IQ scores and many psychological and educational variables and attributes
A form of order in the universe – p. 91 in book
There is a typical, or average value, and there is just as much deviation above as below that middle point in a specific symmetrical pattern.

5. Properties of the Normal Dist.
Unimodel
Symmetrical
Mean, Median, Mode – All at same place
Bell shaped

6. Properties of the Normal Dist.

7. Properties of the Normal Dist.
Has a particular mathematical function
Infinite family of distributions
Goes asymptotic to X axis
Inflection points – 1 SD above and below mean

8. Properties of the Normal Dist.

9. Properties of the Normal Dist.
Areas under portions of the curve are well tabulated – See pp in book
All normal distributions can be converted to the Standard Normal Distribution
z = ( x – m ) / s
Empirical Rule
+/- 1 SD ≈ middle 68%,
+/- 2 SDs ≈ middle 95%
+/- 3 SDs ≈ middle 99%,

10. Properties of the Normal Dist.

11. Percentile Ranks Interactive View of the Normal Distribution
Class Exercises

12. Binomial Distribution
We can use the known properties of the Binomial distribution to calculate the probability of specific kinds of events.
The conditions that must be met:
The event has only two outcomes (success / failure) across a fixed number of trials
The probability of success is known and the same for each trial
The events are independent, no event influences future events

13. Sample Binomial Situations
Flipping a fair coin (head / tail)
Having a baby (boy / girl)
Selecting a card from a fair deck ( red / black)
Shooting a foul shot in basketball
Sampling a product from an assembly line and getting a defective product or a properly made product

14. Binomial Situations
Simulation #1
Simulation #2
Class Exercises

15. Combined Event Probabilities
What is the probability, using two fair dice, of rolling a 4 and a 6?
What is the probability, using two fair dice, of rolling a 4 with one die or a 6 with the other die?
What is the probability of rolling a 4 or a 6 with one roll?
What is the probability, using two fair dice, of rolling two 6s?
Calculations