Late Deliveries: Exploring Normal Distributions
Task
In this lesson, students use the Tuva simulation environment to model delivery times using a Normal Distribution. By choosing appropriate values for the mean and standard deviation and analyzing simulated results with dividers and percent of cases, students estimate probabilities related to “typical” and “late” deliveries. Learning Objectives Students will be able to: Interpret the mean and standard deviation in the context of delivery times Choose reasonable values for μ and σ when modeling a real-world situation Use simulation to generate an empirical Normal distribution Estimate probabilities for ranges and thresholds using dividers and percent of cases Describe how changes in standard deviation affect spread while the mean remains fixed
Introduction A food-delivery company records the delivery time (in minutes) for orders placed in the same neighborhood. Most deliveries arrive close to an average time, but some arrive earlier and some arrive later. The operations team wants to understand: What counts as a typical delivery time? How often deliveries take longer than expected?
Topics and standards: Math, Simulation, Variability, Normal Distribution, Probability & Random Variables, Statistics & AP Statistics, Assessment, AP Statistics