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The Empirical Rule of Normal Distribution

The Empirical Rule of Normal Distribution
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2019-10-10 00:04
FunctionIntegralProbability & Statistics
This example demonstrates the empirical rule of normal distribution, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Key mathematical concepts include normal distribution, standard deviation, and probability. Using GeoGebra commands such as Normal, Integral, and Textfield, the example dynamically shows the normal distribution curve and its probability areas. Suitable for high school and above students to learn probability and statistics.

GeoGebra Commands & Parameters

  1. Normal(0, 1, x, false) → f
  2. Integral(f, -1, 1) → a
  3. Integral(f, -2, 2) → b
  4. Integral(f, -3, 3) → c
  5. Textfield(μ) → InputBox1
  6. Textfield(σ) → InputBox2

AI Drawing Prompt Reference

Draw a standard normal distribution curve and show the probability distribution areas within ±1, ±2, and ±3 standard deviations from the mean. Input the mean and standard deviation to dynamically display the probabilities of 68%, 95%, and 99.7% of the data falling within these ranges.
The prompt above was compiled from the original drawing commands and is for reference only.