1. One coin, many flips
Set the coin's bias and how many times it's flipped per trial. Each trial counts how many heads came up — that count is one bar in the histogram. Run many trials and the histogram's shape appears on its own. This is the binomial distribution — it's not drawn, it's counted.
2. What just happened
Notice: as trials pile up, the jagged bar chart smooths into a predictable bump centered near n × bias. Push flips-per-trial up and bias toward 0.5, and that bump starts looking exactly like the normal "bell curve" — even though nothing here ever drew a bell curve. It assembled itself from thousands of simple yes/no outcomes. That's the Central Limit Theorem in miniature: pile up enough small independent random effects, and the sum looks approximately normal almost regardless of what the small pieces looked like.
3. Why this matters — three connected ideas
The shape is a consequence, not an assumption
A "normal" variable isn't normal by decree — it's normal because it's built from many small independent contributions adding up. Understanding the generator explains why so many unrelated real-world quantities (heights, measurement error, test scores) end up bell-shaped.
Bias shifts the center, sample size sharpens it
Changing the coin's bias moves where the bump sits. Increasing flips per trial doesn't move the center — it narrows the spread relative to n, because random ups and downs increasingly cancel out over more flips.
Rare outcomes aren't impossible, just less counted
The tails of the histogram are trials that landed far from average. They're not errors — they're the expected minority. This is the seed of everything hypothesis testing later asks: "is this outcome an ordinary tail event, or is something else going on?"
One machine, many named distributions
This same coin-flip machine, reused differently, generates the distributions you'll meet later: count heads in one trial → binomial. Count flips until the first head → geometric. Count many small independent effects summed together → normal. Different questions asked of the same randomness.