This document is an extended version of an abstract for a talk, with approximately the same title, to be held at the 7th Joint Statistical Meeting of the Deutsche Arbeitsgemeinschaft Statistik, from 24 to 28 March 2025 in Berlin. Here ``teachable'' is meant to apply to people ranging from sufficiently advanced high school pupils to university students in mathematics or statistics: For understanding most of the proposed approximation results, it should suffice to know binomial laws, their means and variances, and the standard normal distribution function (but not necessarily the concept of a corresponding normal random variable). Of the proposed approximations, some are well-known (at least to experts), and some are based on teaching experience and research at Trier University.

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