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.

翻译：本文是即将于2025年3月24日至28日在柏林举行的第七届德国统计学会联合统计会议中一场报告摘要的扩展版本，报告标题与本标题大致相同。此处“可教学”意指适用于从具备足够基础的高中生到数学或统计学专业大学生的群体：要理解本文提出的大多数近似结果，仅需掌握二项分布律、其均值与方差以及标准正态分布函数的知识（而不必掌握对应正态随机变量的概念）。在所提出的近似方法中，部分已广为人知（至少对专家而言），部分则基于特里尔大学的教学经验与研究实践。