Probability Distributions

Probability Distributions - The Normal Probability...

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

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