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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?

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Z-Scores (Chapter 6)


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z scores chapter 6
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
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
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
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
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