The Normal Distribution | 正态分布

📚 The Normal Distribution | 正态分布

The normal distribution is one of the most important continuous probability distributions in A-Level Mathematics. It models continuous data that cluster symmetrically around a mean, and it is widely used in statistics, science and everyday measurements. This article covers the Edexcel A-Level normal distribution topic, including standardising, probabilities, inverse problems, sample means and the normal approximation to the binomial distribution.

正态分布是 A-Level 数学中最重要的连续型概率分布之一。它为围绕均值对称聚集的连续数据建模，广泛用于统计、科学和日常测量。本文涵盖 Edexcel A-Level 正态分布主题，包括标准化、概率计算、逆问题、样本均值以及二项分布的正态近似。

1. Definition and Shape of the Normal Distribution | 正态分布的定义与形状

A continuous random variable X follows a normal distribution if its probability curve is a bell-shaped curve that is symmetric about the mean μ. The curve has a single maximum at x = μ, and it extends indefinitely in both directions, approaching but never touching the horizontal axis.

若连续型随机变量 X 的概率曲线是一条关于均值 μ 对称的钟形曲线，则 X 服从正态分布。曲线在 x = μ 处取得唯一最大值，并向两侧无限延伸，接近但永不触及水平轴。

We write X ~ N(μ, σ²), where σ² is the variance and σ

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