The central limit theorem says that if you average n independent draws from almost any population, the distribution of that average approaches Normal(μ, σ²/n) — no matter how lumpy or lopsided the population was.
Averaging only ever sees the first two moments, μ and σ — every other detail of the shape you paint is forgotten in the pour.
The bell's width is the standard error, σ/√n: quadruple the sample size and the pile stands exactly half as wide, so halving uncertainty always costs four times the data. The forge's ruler is locked to the mold, not to n, so that shrinking is real and not an illusion of rescaling — switch the window to Fit bell and it zooms with the pile instead, which is handy for inspection but hides the law.
The shaded band around the dashed curve is the prediction's own scatter, ±2√E ingots per column — wide over the first few dozen batches, tight once the pile is deep.
Mind the classic trap: your data never turn normal — the mold keeps the shape you painted, and only the distribution of the mean is forged into the bell.
The foundry's furnace faltered mid-pour. The lesson continues without it — everything you have learned so far is safe.