Week 6 · Suggested 75 minutes · First-pass draft
What the central limit theorem actually says
Distinguish raw observations from their averages using repeated simulation.
Applied assignment, not a stored grade. Instructions and model checks are provided for self-study or instructor adaptation. Work is not transmitted to this site.
What you will do
- Predict the distribution of single values drawn from a right-skewed exponential model.
- In the central-limit laboratory, compare sample means from n=1, n=5, n=30, and n=80.
- Record the observed standard deviation of means and compare it with the theoretical standard error.
- Explain why the original exponential population does not become normal.
What to submit
Four comparative plot descriptions, a numerical summary table, and a correct statement of the theorem's assumptions.
Self-check before finishing
Increasing n makes the distribution of sample means narrower, under finite-variance independent sampling.
Assigned reading
Use density areas, normal probabilities, and the central limit theorem.
Instructor discussion guidance
Do not accept the claim that the raw data become normally distributed after thirty observations.
Print a predict–experiment–explain worksheet → · Open browser R →