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

作业