Chapter 5: Probability, Normal Distributions, and z Scores

What is probability?

* Frequency of times an outcome occurs/total # of outcomes
* *p*
* Varies between 0-1
* Never be negative
* p(x) = f(x)/sample space

What is normal distribution?

* Theoretical distribution with data that are symmetrically distributed around the mean, median, mode
* scores closer to the mean are more probable, or likely, than other scores further from the mean


1. Mathematically defined
2. Theoretical
3. Mean, median, mode are all located at 50th percentile
4. Symmetrical
5. Can equal any value
6. SD can equal any positive value
7. Total area under the curve is 1.0
8. Tails are asymptotic

What is standard normal distribution?

* normal distribution with a M = 0 and SD = 1
* Distributed in z score units along the x-axis

What are z Scores?

value on the x-axis of a standard normal distribution. The numerical value specifies the distance or SD of a value from the mean

What are the formulas for standard normal transformation?

* Population of scores: z = (x - mu)/SD
* Sample of scores: z = (x - M)/SD