# PY 211 Lecture Notes - Lecture 8: Community Reinvestment Act, Normal Distribution, Standard Deviation

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Probability and Normal Distributions
What Does Standard Deviation Tell Us?
A. Empirical rule
a. For normal distributions with an mean and any variance:
i. Mean +/- one SD includes at least 68% of all scores
ii. Mean +/- two SDs at least 95% of all scores
iii. Mean +/- three SDs at least 99.7% of all scores
From Frequency Distributions to Probability
Frequency polygon of a normal distribution (proportion)
o Describes what it is
o Can use to estimate probable scores
How does the standard deviation affect the confidence in your estimate?
o Smaller SDs
o Larger SDs
The Beauty of the Normal Distribution
No matter what the mean is
No matter what the SD is
Proportions remain the same (68%, 95%, 99.7%)
Normal Distribution in Behavioral Science
I. Measurements of behavior, attitudes, thoughts
a. Form normal distributions (approximately)
b. Mean = median = mode
II. Use properties of normal distribution to estimate likelihood (probability)
a. Given a score of x, how similar is it to other scores in distribution?
b. Is this a likely score, given a particular distribution?
Characteristics of Normal Distribution
I. Theory
a. Mathematically defined
b. Theoretical
c. Tails are asymptotic (tails never reach 0 frequency)
d. Area under curve is 1.0
II. Properties
a. Mean, median, mode are all at 50% percentile
b. Symmetrical
c. Mean and standard deviation can have any values (positive values only)
Clicker: relative frequency is on the y-axis
Standard Normal Distribution
I. Transform all x scores to z scores
a. Z = x-M / SD
b. Z-score transformation
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## Document Summary

Frequency polygon of a normal distribution (proportion: describes what it is, can use to estimate probable scores. How does the standard deviation affect the confidence in your estimate: smaller sds, larger sds. Proportions remain the same (68%, 95%, 99. 7%) Normal distribution in behavioral science: measurements of behavior, attitudes, thoughts, form normal distributions (approximately, mean = median = mode. Characteristics of normal distribution: theory, mathematically defined, theoretical, tails are asymptotic (tails never reach 0 frequency, area under curve is 1. 0. Properties: mean, median, mode are all at 50% percentile, symmetrical, mean and standard deviation can have any values (positive values only) Standard normal distribution: transform all x scores to z scores, z = x-m / sd, z-score transformation, z-score distribution (standard normal distribution, mean always translate to a z score of 0. Transformed mean and standard deviation: new mean: m = 0, new sd = 1.

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