Interactive Visualization of a Univariate Gaussian Distribution

This example demonstrates how a univariate Gaussian (normal) distribution’s probability density function relates to probability obtained as an integral over an interval, visually highlighting the area under the curve between endpoints. The key mathematical ideas are the parameterized Gaussian pdf f(x), the mean μ and standard deviation σ (showing how shifting and scaling affect the curve), the central location concept (often linked to median/center due to symmetry), and computing probabilities using definite integrals. In GeoGebra construction, it uses IntegralBetween to evaluate the integral from a to b, Intersect to determine relevant intersection points, and Segment to create interval boundaries and supporting geometric segments. Main objects include μ, σ, f, a, and b, along with equation/graph elements such as eq1, A, B, and g for the curve and auxiliary structure, while text1–text4 provide annotations for the key quantities. Suitable for upper secondary through early university courses in probability & statistics and calculus, especially when connecting definite integrals with probability.