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Z-Score Calculator and Visualizer

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About This MicroSim

Calculate and visualize z-scores with an interactive normal distribution curve.

How to Use

  • Drag the marker along the curve to change the raw value (x)
  • Use preset buttons to load different real-world examples (IQ, SAT, Heights)
  • Adjust μ (mean) and σ (standard deviation) sliders to change distribution parameters
  • Watch the z-score calculation update in real time

Key Insights

  • Z-score formula: z = (x - μ) / σ
  • Z-score tells you how many standard deviations a value is from the mean
  • Positive z-scores are above the mean; negative z-scores are below
  • |z| < 2 is typical; |z| > 2 is unusual; |z| > 3 is very rare

Lesson Plan

Learning Objective

Students will calculate z-scores from raw values and interpret their meaning in the context of a normal distribution (Bloom's Taxonomy: Applying, Analyzing).