====== 第四章：z分数、概率、正态分布和二项分布 ======

====== Chapter 4: Z-scores, probabilities, normal distributions, and binomial distributions ======

=)**本章概览 (Guide)**：
在本章中，我们学习了z分数、概率这两个概念，并将他们运用于两类分布：正态分布与二项分布。\\ In this chapter, we learned the concepts of Z-score and probability, and applied them to two types of distributions: normal distribution and binomial distribution.
  * 在引入z分数前，很难将均值、标准差不同的正态分布进行比较。引入z分数后，我们将原分布均转换为标准分布，在标准分布上进行比较。\\ It is difficult to compare normal distributions with different means and standard deviations before introducing Z-score. After introducing Z-score, we convert the original distribution to a standard distribution and compare it in the standard distribution version.
  * 概率是推论统计所必需的概念, 根据样本的信息对总体作出判断。\\ Probability is a necessary concept for inferential statistics, which judges the population based on the information of the sample.
  * 通过z分数，我们可以求解正态分布的百分位数，并通过正态分布表将z值与概率一一对应。\\ By using the Z-score, we can calculate the percentile of a normal distribution and use the normal distribution table to correspond the z-value to the probability one by one.
  * 二项分布在一定条件下可以近似为正态分布，同样可以利用z值和概率求解。\\ The binomial distribution can be approximated as a normal distribution under certain conditions, and can also be solved using Z-values and probabilities.

:!:**学习要点 (Learning points)**：
  - 学会利用z分数进行原分布与标准分布之间的互相转换\\ Learn how to use z-scores to convert between the original distribution and the standard distribution
  - 学会利用随机取样、回置取样来计算概率，并通过样本概率推测总体分布\\ Learn how to use random sampling and back sampling to calculate probability, and infer population distribution through sample probability
  - 掌握正态分布的公式与基本特征，利用查表与插值法计算百分位数\\ Master the formulas and basic characteristics of normal distribution, and use table lookup and interpolation methods to calculate percentiles
  - 掌握正态分布中1σ, 2σ, 3σ内的百分比率\\ Master the percentage rate in 1σ, 2σ and 3σ of normal distribution.
  - 理解二项分布的公式，并掌握将二项分布近似为正态分布的条件与方法\\ Understand the formula of binomial distribution and master the conditions and methods for approximating binomial distribution to normal distribution 

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**目录**
  * [[z分数|z分数 (Z-score)]]
  * [[概率| 概率 (Problarity)]]
  * [[Normal-distribution|正态分布 (Normal distribution)]]
  * [[二项分布|二项分布 (Binomial distribution)]]

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**作业**
  * [[第四章作业|2023作业 (Homework of 2023)]]
  * [[2024homework4|2024作业 (Homework of 2024)]]