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Properties of Normal Distribution

Properties of Normal Distribution
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2019-09-15 17:15
FunctionCalculusDerivativeProbability & StatisticsGraphing
In collections Probability distributions with GeoGebra
This example demonstrates the properties of the normal distribution curve and its related characteristics. It involves core mathematical concepts such as Normal Distribution, Parabola, Tangent Line, Conditional Probability, Power Functions, and Trapezium. The construction utilizes GeoGebra commands like Normal, Integral, and If, with objects including μ, σ, f, koh_1, a, koh, b, text elements (text1, text2), points (A, B, C, D), and others (paik, text3, text4, text5, paik2, paik3). It is suitable for high school students and educators for teaching and exploring the graphical representation of the normal distribution.

GeoGebra Commands & Parameters

  1. Normal(μ, σ, x, false) → f
  2. Normal(μ, σ, (σ * koh_1) + μ) → a
  3. Integral(Normal[μ, σ, x, false], -30, (σ * koh) + μ) → b
  4. If(koh ≤ 1, (paik2, 0.05 + (0.015 * (koh + 2))), (μ, 0.03 + (0.015 * 4))) → paik3

AI Drawing Prompt Reference

Draw a normal distribution curve and illustrate its relationship with a parabola, tangent line, conditional probability, power functions, and trapezium. Include parameters μ and σ, calculate the area under the curve using integration, and adjust specific point positions based on parameter koh for educational purposes to showcase the graphical features of the normal distribution.
The prompt above was compiled from the original drawing commands and is for reference only.