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lab3notes - Slide 1 Lab 3 z-Scores and the Normal Curve...

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Slide 1 Lab 3 z-Scores and the Normal Curve ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 2 Learning Objectives Define a z-score. Calculate z-scores. State the mean and SD of the Standard Normal Curve. Use tabled values of the normal curve to estimate percentages of a distribution. Graph Distributions. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 3 What is a z-score? Z-score defined. A z-score tells the location of an observation in terms of standard deviations from the mean. If a z-score is zero, it’s on the mean. If a z-score is positive, it’s above the mean. If a z-score is negative, it’s below the mean. The value of the z-score tells how many standard deviations above or below the mean it is. A z- score of 2 is 2 SDs above; -1 is 1 SD below. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________
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Slide 4 Z-score formulas To find a z-score, subtract the mean from the score and divide by the SD. A z-score for a population: A z-score for a sample: σ µ = X z s X X z = ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 5 Computing z-scores from raw scores -.5 4 -2 10 8 1.25 4 5 3 8 .5 4 2 3 5 1 2 2 3 5 X X X s X s X X z = ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 6 Computing z-scores What is z? =10, =8, s=4, z = ? A: .5 =8, =10, s=2, z=? A: -1 =20, =15, s=5, z =? A: 1 X X X X X X ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________
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Slide 7 Computing raw scores from z-scores -- Formulas To find a raw score, multiply the z-score by the SD and then add the mean. Population formula: Sample formula: µ σ + = z X X zs X + = ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 8 Computing raw scores from z-scores -- Examples -5 -6 1 4 -1.5 8 0 8 2 0 -4 -6 2 3 -2 5 3 2 3 1 X=zs+ zs s z X X ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 9 Computing raw scores What is X?
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