Normal Distribution of MPG & Weekly Cost

This GeoGebra example demonstrates how to model the relationship between car fuel efficiency (MPG) and weekly fuel cost using a normal distribution. It allows users to interactively adjust the mean, standard deviation, and interval bounds to observe how the area under the normal curve changes, representing cumulative probabilities. Core mathematical concepts include normal distribution, probability density function, definite integrals for probability areas, the effects of mean and standard deviation on curve shape, and the use of geometric mean and derivatives in parameter sensitivity. The construction uses GeoGebra commands such as Normal to generate the curve, Integral to compute shaded areas, and Textfield with LaTeX for dynamic input and formula display. Key objects include xl (mean), stdev (standard deviation), xh/xl (bounds), zUp/zDwn (z-scores), and area variables a, b, c. This resource is suitable for high school to university-level statistics and probability courses, as well as applied economics for cost forecasting, helping learners grasp the practical application of normal distributions in real-world data.