The Normal distribution is the most appropriate model for representing the actual arrival times of a bus on a fixed schedule. The scheduled arrival time acts as the mean (average) of the distribution. Actual arrivals will naturally vary due to factors like traffic, weather, and passenger load. These variations cause most arrival times to cluster closely around the scheduled time, with fewer arrivals occurring significantly early or late. This symmetric, bell-shaped clustering around a central value is the defining characteristic of a Normal distribution, making it the most effective model for this scenario.

A. Binomial: This distribution models the number of successes in a set number of discrete trials (e.g., heads in 10 coin flips), not a continuous variable like time.

B. Exponential: This distribution models the time between independent, random events (e.g., time until the next customer arrives), not deviations from a scheduled event.

D. Poisson: This distribution models the count of events occurring in a fixed interval (e.g., number of buses arriving in an hour), not the precise arrival time of a single bus.

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1. MIT OpenCourseWare. (2014). 18.05 Introduction to Probability and Statistics

Spring 2014. Lecture 13: Central Limit Theorem. Massachusetts Institute of Technology. The notes describe the Normal distribution as a model for phenomena resulting from the sum of many small

independent random effects

which accurately describes the various factors (traffic

passengers

etc.) causing deviations in a bus's scheduled arrival time. (See Section 2

"The Bell Curve").

2. Stanford University. (2023). CS109: Probability for Computer Scientists

Lecture Notes 12: Normal Distribution. The lecture notes explain that the Normal distribution is often used to model real-world continuous variables where values cluster around a mean

such as measurement errors. The deviation of a bus's arrival time from its schedule is a form of measurement error. (See "Normal Random Variable" section).

3. University of California

Berkeley. (2021). STAT 20: Introduction to Probability and Statistics

Lecture 17: The Normal Distribution. The course material explicitly states that the Normal distribution is a suitable model for continuous random variables where the data is expected to be symmetric and centered around a mean

which is the expected pattern for bus arrivals relative to a schedule. (See "Properties of the Normal Curve").