使用表格查找标准正态分布Z的概率
本节将学习如何使用表格来查找标准正态分布Z的概率。标准正态分布是统计学中最重要的分布之一，具有均值0和标准差1的特殊性质。
This section will teach you how to use tables to find probabilities for the standard normal distribution Z. The standard normal distribution is one of the most important distributions in statistics, with the special properties of mean 0 and standard deviation 1.
通过掌握标准正态分布的概率计算方法，我们可以解决许多实际统计问题，包括质量控制、医学研究、社会科学等领域的数据分析。
By mastering the probability calculation methods for the standard normal distribution, we can solve many practical statistical problems, including data analysis in quality control, medical research, social sciences, and other fields.
标准正态分布Z具有均值μ = 0和方差σ² = 1的特殊性质，记作Z ~ N(0, 1²)。这是所有正态分布的标准形式。
The standard normal distribution Z has the special properties of mean μ = 0 and variance σ² = 1, written as Z ~ N(0, 1²). This is the standard form of all normal distributions.
正态分布表格提供了P(Z < z)的值，我们可以通过这些表格查找各种z值对应的概率，这是计算标准正态分布概率的主要方法。
Normal distribution tables provide values of P(Z < z), allowing us to find probabilities corresponding to various z values. This is the main method for calculating standard normal distribution probabilities.
标准正态分布具有对称性质，P(Z < -a) = P(Z > a) = 1 - P(Z < a)。利用这个性质可以计算负z值的概率。
The standard normal distribution has symmetry properties: P(Z < -a) = P(Z > a) = 1 - P(Z < a). This property can be used to calculate probabilities for negative z values.
\[Z \sim N(0, 1^2)\]
其中μ = 0，σ² = 1
Where μ = 0, σ² = 1
\[\Phi(a) = P(Z < a)\]
Φ(a)是P(Z < a)的简写记号
Φ(a) is shorthand notation for P(Z < a)
\[P(Z < -a) = P(Z > a) = 1 - P(Z < a)\]
利用对称性质计算负z值的概率
Use symmetry properties to calculate probabilities for negative z values
\[P(a < Z < b) = P(Z < b) - P(Z < a)\]
计算Z在区间(a, b)内的概率
Calculate the probability that Z lies in the interval (a, b)