Probability Distributions

# Probability Distributions - The Normal Probability...

This preview shows pages 1–6. Sign up to view the full content.

The Normal Probability  Distribution and Z-scores Using the Normal Curve to Find Probabilities

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Carl Gauss The normal probability distribution or the “normal curve” is often called the Gaussian distribution, after Carl Friedrich Gauss, who discovered many of its properties. Gauss, commonly viewed as one of the greatest mathematicians of all time (if not the greatest), is honoured by Germany on their 10 Deutschmark bill. From http://www.willamette.edu/~mjaneba/help/normalcurve.html
Properties of the Normal  Distribution: Theoretical construction Also called Bell Curve or Gaussian Curve Perfectly symmetrical normal distribution The mean (µ) of a distribution is the midpoint of the curve The tails of the curve are infinite Mean of the curve = median = mode The “area under the curve” is measured in standard deviations (σ) from the mean (also called Z). Total area under the curve is an area of 1.00

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Theoretical Normal Curve (from http://www.music.miami.edu/research/statistics/normalcurve/images/normalCurve1.gif
Properties (cont.) Has a mean µ = 0 and standard deviation σ = 1. General relationships: ±1 σ = about 68.26% ±2 σ = about 95.44% ±3 σ = about 99.72%* *Also, when z=±1 then p=.68, when z=±2, p=.95, and when z=±3, p=.997 -5 -4 -3 -2 -1 0 1 2 3 4 5 68.26% 95.44% 99.72%

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/24/2011 for the course MATH 221 taught by Professor Bethdodson during the Spring '10 term at DeVry Chicago.

### Page1 / 20

Probability Distributions - The Normal Probability...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online