Instructional Module

Distributions & Probability

01. Concept Review

Before entering the lab, review the fundamental differences between these two core statistical concepts.

The Binomial Distribution

Type: Discrete (Whole numbers only).

Scenario: Used when counting "successes" in a fixed number of independent trials (e.g., flipping a coin 10 times).

Key Parameters: n (number of trials) and p (probability of success).

The Normal Distribution

Type: Continuous (Fluid, smooth data).

Scenario: The famous "Bell Curve." Nature loves this distribution (heights, test scores, errors).

Key Parameters: μ (Mean/Center) and σ (Standard Deviation/Spread).

The Central Limit Theorem

The Magic: Even if data starts as Binomial (discrete), if you have a large enough sample size (n), the graph will smooth out and begin to look exactly like a Normal Distribution.

02. Convergence Lab

Use the sliders below to adjust the parameters of a Binomial experiment. Observe how the discrete bars (Binomial) align with the smooth bell curve (Normal approximation) as N increases.

Binomial (Discrete Bars)
Normal Approximation (Continuous Curve)