What is the chance of hitting every green light on my route?

AI SLAI HLAA SLAA HL Accessible Also in: Statistics, Modelling

Research question

Using measured cycle times for the traffic lights on my route to school, what is the probability distribution of my total waiting time, and does it match my recorded journeys?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Your commute is a sequence of random waits. Measuring the lights and modelling the waiting time turns daily frustration into a probability distribution you can test.

The mathematics you'll need

Uniform and mixed discrete-continuous distributions
Expected value of waiting time
Sum of independent random variables (simulation)
Comparing a model with recorded data

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Time the red and green phases of each light on your route (repeatedly), then record waiting times on 20+ journeys.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Model a single light: P(wait) and expected wait.
Combine lights assuming independence.
Simulate the total waiting distribution.
Compare with recorded journeys.
Reflect: lights are often coordinated (a “green wave”), so independence fails.

Pitfalls that cost marks

Assuming independence without testing it.
Timing phases only once.
Recording journeys at different times of day.

Showing personal engagement

Use your actual route.
Test whether cycling faster or slower changes your total wait.
Investigate a coordinated sequence and model it.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Model coordinated lights with a fixed offset and find the speed that gives a green wave.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).