normal - Random Variables and Probability Distributions...

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Random Variables and Probability Distributions Random Variables - Random responses corresponding to subjects randomly selected from a population. Probability Distributions - A listing of the possible outcomes and their probabilities (discrete r.v. s ) or their densities (continuous r.v. s ) Normal Distribution - Bell-shaped continuous distribution widely used in statistical inference Sampling Distributions - Distributions corresponding to sample statistics (such as mean and proportion) computed from random samples
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Normal Distribution Bell-shaped, symmetric family of distributions Classified by 2 parameters: Mean ( μ ) and standard deviation ( σ ). These represent location and spread Random variables that are approximately normal have the following properties wrt individual measurements: Approximately half (50%) fall above (and below) mean Approximately 68% fall within 1 standard deviation of mean Approximately 95% fall within 2 standard deviations of mean Virtually all fall within 3 standard deviations of mean Notation when Y is normally distributed with mean and standard deviation : ) , ( ~ N Y
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Normal Distribution 95 . 0 ) 2 2 ( 68 . 0 ) ( 50 . 0 ) ( + - + - = σ μ Y P Y P Y P
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Example - Heights of U.S. Adults Female and Male adult heights are well approximated by
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normal - Random Variables and Probability Distributions...

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