Z-Scores (Chapter 6) Equation for Z can be solved forwards or backwards: Raw score  z-score  probability Xi  Zi  probability What score is necessary to be in the top or bottom x-percentage of The distribution? Look up the z-score associated with that probability Probability  z-score  raw score For proportions below The mean, use negative Z-scores

Finding The Proportion Between A Range Of Scores Translate the raw scores to z-scores: If the range spans the mean, add the areas in Column B If the range is on one side of the mean, subtract the smaller area From the larger area (using Column C) Use Z-scores to find either the Proportion or the Probability

What Proportion OF The Population Has An IQ ? μ = 100; σ = 15 Area between mean (X=100, Z=0) and X=110 (Z=0.67) Column B Z= >.2486 (Area =Probability) Area between mean (X=100, Z=0) and X=90 (Z=-0.67) Column B Z= >.2486 (Area =Probability) = > 49.72% (~50%) of Population

What Proportion OF The Population Has An IQ 70-90? μ = 100; σ = 15 Area between mean (X=100, Z=0) and X=70 (Z=-2.00) Column C Z= > (Area =Probability/Proportion; 2.28%) Area between mean (X=100, Z=0) and X=90 (Z=-0.67) Column C Z= >.2486 (Area =Probability/Proportion; 24.86%) = > 22.86% of Population

Finding The Scores Which Define An Extreme (2-Tail) Group What is the range of heart rates for 95% of the population? μ = 71; σ = 9 Upper ScoreLower Score X = μ + Z * σX = μ - Z * σ = 71 + (1.96)*9 = 71 - (1.96)*9 = 88.6 = 53.4