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... I'm not sure the Geiger counter is the best pedagogical approach. Unlike
drawing numbers from an urn, where the numbers are imagined to pre-exist,
the Geiger-counter numbers are themselves some sort of average of a
statistical process. This complicates the terminology (what "mean" are you
talking about? which "process" are you talking about?) and makes the
concepts look more complicated than they really are. And Geiger tubes (and
radioactive sources) are not available to the typical science teacher.
Following the spirit of Gosset, why not just do a Monte Carlo with a
spreadsheet? That's available to the typical science teacher.