Central Limit Theorem (Galton)
Drop dynamic particles through a physics-enabled Galton Board. Watch the Binomial Distribution organically construct and flawlessly approximate a continuous Normal Curve.
THE MAGIC OF AVERAGES
The **Central Limit Theorem (CLT)** states that for a large enough sample size (), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
THE GALTON BOARD
A Galton Board demonstrates the CLT visually. As beads drop through a forest of pegs, each individual path is a random walk, but the collective result always forms a bell-shaped normal distribution.
AP EXAM CONNECTION
Unit: Unit 5: Sampling Distributions (Topic 5.2)
Learning Objective: UNC-4.B
COMMON MISCONCEPTIONS
- Applying CLT to small sample sizes from non-normal populations.
KEY TAKEAWAYS
- Requires n >= 30.
- Normalizes the mean.
- Works for any population shape.
PRACTICE QUESTIONS
Q1 (CONCEPTUAL): Does the CLT say the population distribution becomes normal as n increases?
Show Answer & Explanation
Answer: No.
Explanation: The CLT only describes the **sampling distribution** of the mean, not the distribution of individuals in the population.
