Z-Scores (Chapter 6)

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# Z-Scores (Chapter 6) - PowerPoint PPT Presentation

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?

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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 90-110?

μ = 100; σ = 15

• Area between mean (X=100, Z=0) and X=110 (Z=0.67)
• Column B
• Z=0.67 --> .2486 (Area =Probability)
• Area between mean (X=100, Z=0) and X=90 (Z=-0.67)
• Column B
• Z=-0.67 --> .2486 (Area =Probability)
• 0.2486 + 0.2486 = .4972 --> 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=-2.00 --> 0.0228 (Area =Probability/Proportion; 2.28%)
• Area between mean (X=100, Z=0) and X=90 (Z=-0.67)
• Column C
• Z=-0.67 --> .2486 (Area =Probability/Proportion; 24.86%)
• 0.2486 - 0.0228 = .2286 --> 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 * σ X = μ - Z * σ
• = 71 + (1.96)*9 = 71 - (1.96)*9
• = 88.6 = 53.4