lab3zf03 - Lab 3 z-Scores the Normal Curve and Computer...

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Unformatted text preview: Lab 3 z-Scores, the Normal Curve, and Computer Graphs of Distributions 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. 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. 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- = Computing z-scores from raw scores 5 3 2 2 1 5 3 2 4 .5 8 3 5 4 1.25 8 10-2 4-.5 X X X- s X s X X z- = 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 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 + = Computing raw scores from z-scores -- Examples z s zs X=zs+ 1 3 2 3 5-2 3 2-6-4 2 8 8-1.5 4 1-6-5 X X Computing raw scores What is X?...
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lab3zf03 - Lab 3 z-Scores the Normal Curve and Computer...

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