Normal Distribution Curve for Hypothesis Testing Areas

This example demonstrates how changing parameters in a normal distribution turns hypothesis-testing quantities into a clear geometric picture: the curve and its critical regions (tail/interval areas) under a chosen significance level. It centers on the key concepts of the normal distribution (mean μ and standard deviation σ), probability density and distribution behavior, quantiles via the inverse function, and the interpretation of p-values/significance through the area under the curve. Construction in GeoGebra uses Textfield for labeling (μ, σ, α, and intermediate symbols), InverseNormal to compute critical points from input probabilities (e.g., invϕ_1, invϕ_2, invϕ_3), Normal to define the normal distribution curve/functions, Segment to draw vertical boundary lines and interval markers, and Integral to compute the shaded or selected areas corresponding to the test regions (various area/region objects such as A, C, D and related items). Suitable for high school to introductory college statistics/probability, and useful for classroom demonstrations and self-study to connect hypothesis testing logic directly with “critical values + tail probabilities = area under the normal curve.”