Coding the Normal Distribution: Visualizing Probability with Inverse Functions

This example demonstrates how to use GeoGebra’s programming-style commands to connect the normal distribution’s density, cumulative probability, and quantile values in a single interactive visualization. The key ideas are the normal distribution parameters (mean μ and standard deviation σ), the probability density function, the cumulative distribution function (CDF), and especially the inverse CDF (InverseNormal) for mapping a probability level to the corresponding x-value (a quantile). Construction highlights extracted from the GeoGebra summary include using If for piecewise/conditional logic, Integral to compute cumulative probability via area under the curve, and InverseNormal to derive the quantile from a given probability. The setup uses parameter objects and interval endpoints, along with text/label objects to annotate critical values such as probability regions and quantile markers. Suitable for high school to undergraduate probability & statistics lessons, workshops, and math-in-code explorations focusing on CDF/inverse-CDF relationships and interactive graphing.