Normal Distribution Curve and Area-Probability via Integration

This GeoGebra example demonstrates how the normal (Gaussian) distribution density changes with the parameters μ (mean) and σ (standard deviation), and how probability over an interval corresponds to the area under the curve. Key concepts include the normal probability density function f(x), the cumulative/integrated quantity F(x), and the interpretation of definite integrals as probability mass. The construction uses the GeoGebra command Integral with objects a, b, μ, σ, f, c, and F: a and b serve as the integration bounds, f represents the density function, and F represents the resulting accumulated/integral value. The point/object c helps highlight key locations on the curve so learners can visually connect “area under f” with the computed integral. Suitable for high-school advanced study and early university topics in probability & statistics, as well as calculus-based understanding of definite integrals and function graphs.