7.3 Using Tables to Find the Value of z Given a Probability

7.3 反向查找z值 - 核心知识点总结

1. 基本概念 / Basic Concepts

反向查找定义：根据给定的概率值查找对应的z值

Inverse Lookup Definition: Finding the corresponding z-value given a probability value

• 给定概率p，查找z值使得P(Z > z) = p

• Given probability p, find z-value such that P(Z > z) = p

• 或者：P(Z < z) = p

• Or: P(Z < z) = p

2. 查找工具 / Lookup Tools

优先级顺序 / Priority Order

3. z值符号判断规则 / Rules for Determining z-value Signs

4. 解题步骤 / Problem-Solving Steps

5. 对称性应用 / Symmetry Applications

重要对称性质：

Important symmetry properties:

• P(Z > a) = P(Z < -a)

• P(Z < a) = P(Z > -a)

• 如果P(Z > 1.286) = 0.1，那么P(Z < -1.286) = 0.1

• If P(Z > 1.286) = 0.1, then P(Z < -1.286) = 0.1

6. 常见问题类型 / Common Problem Types

类型1：P(Z < a) = p

解题方法：

类型2：P(Z > a) = p

解题方法：

类型3：近似值问题

解题方法：

7. 重要公式总结 / Important Formula Summary

基本关系：

Basic relationships:

• P(Z < a) + P(Z > a) = 1

• P(Z < -a) = P(Z > a) = 1 - P(Z < a)

• P(Z > -a) = P(Z < a)

8. 考试技巧 / Exam Tips

考试注意事项 / Exam Precautions

始终先检查百分比点表 - 这是专门为此目的设计的
Always check percentage points table first - It's specifically designed for this purpose
注意z值的符号 - 这是最容易出错的地方
Pay attention to z-value signs - This is where mistakes most commonly occur
使用图表帮助理解 - 绘制图表可以避免很多错误
Use diagrams to help understanding - Drawing diagrams can prevent many mistakes
验证答案的合理性 - 检查答案是否符合常识
Verify answer reasonableness - Check if the answer makes sense

9. 常见错误 / Common Mistakes

避免这些错误 / Avoid These Mistakes

10. 练习建议 / Practice Recommendations

提高技能的建议 / Suggestions for Skill Improvement

多做不同类型的题目 - 熟悉各种问题类型
Practice different types of problems - Familiarize with various problem types
熟练掌握表格使用 - 提高查找效率
Master table usage - Improve lookup efficiency
练习绘制图表 - 增强可视化理解
Practice drawing diagrams - Enhance visual understanding
注意细节和符号 - 避免粗心错误
Pay attention to details and signs - Avoid careless mistakes

7.3 Using Tables to Find the Value of z Given a Probability - 知识点总结