Every fish has a fixed length, drawn once from a hidden, strongly right-skewed distribution — many little fish, a long tail of big ones. A fish's position wanders completely independently of its length, so the fish that happen to be inside the net are a fair i.i.d. sample of size n from that length distribution.
Each brass token is one sample mean, x̄. Stack enough of them and the central limit theorem takes over: x̄ ≈ Normal(μ, σ/√n), a bell centered on the pond's true mean μ — no matter how lopsided the pond itself is.
The bell's width is the standard error, σ/√n. Quadruple the net (and n) and the pile stands exactly half as wide — halving your uncertainty always costs four times the sample.
Mind the classic trap: the pond's spread is σ; the pile's spread is σ/√n. Different questions, different numbers. Your individual fish never turn normal — only their averages do.
The census net snagged mid-haul. The lesson continues without it — everything you have learned so far is safe.