Standard Normal Distribution and Inverse Phi

Standard Normal Distribution and Inverse Phi
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2016-04-12 20:47
This example demonstrates the standard normal distribution curve and its inverse function Phi, including properties and graphical representation. Core math concepts involve the standard normal distribution, cumulative distribution function (Phi), its inversion, and integral calculations. Construction uses GeoGebra commands like Point, Line, Integral, and Text to plot the distribution, integral area, and annotations, with objects such as function f, z_a, z_b, xaxis, P, c_1, text2, probexp, text1, text4. Suitable for high school and above students learning probability and statistics, focusing on normal distribution applications and inversion.

GeoGebra Commands & Parameters

  1. Point(xAxis) → z_a
  2. Point(xAxis) → z_b
  3. Line(z_a, z_b) → xaxis
  4. Integral(f, x(z_a), x(z_b)) → P
  5. Text(((("ϕ(" * x(z_b)) * ")=") * text2)) → text1
  6. Text(((("P(X<" * x(z_b)) * ")=") * text2)) → text4