normal distribution table

简明释义

正态分布表

英英释义

例句

1.In statistics class, we learned how to use the normal distribution table (正态分布表) to determine z-scores.

在统计课上，我们学习了如何使用正态分布表来确定z分数。

2.When analyzing test scores, the normal distribution table (正态分布表) is essential for interpreting results.

在分析考试成绩时，正态分布表对于解释结果是必不可少的。

3.The normal distribution table (正态分布表) helps in understanding the distribution of data in a bell curve.

使用正态分布表可以帮助理解数据在钟形曲线中的分布。

4.To find the probability of a score being below a certain value, you can refer to the normal distribution table (正态分布表).

要找到某个分数低于特定值的概率，可以参考正态分布表。

5.Researchers often rely on the normal distribution table (正态分布表) to make predictions based on sample data.

研究人员常常依赖正态分布表根据样本数据进行预测。

作文

Understanding the concept of a normal distribution table is crucial in statistics and data analysis. A normal distribution table, also known as the Z-table, provides the probabilities associated with the standard normal distribution, which is a bell-shaped curve that represents the distribution of many types of data. This table allows statisticians to determine how likely it is for a value to fall within a certain range of a normal distribution. The normal distribution is defined by its mean and standard deviation. The mean is the average of the data set, while the standard deviation measures the spread or dispersion of the data points around the mean. When data is normally distributed, approximately 68% of the values fall within one standard deviation from the mean, about 95% fall within two standard deviations, and around 99.7% fall within three standard deviations. This property is known as the empirical rule or the 68-95-99.7 rule.To illustrate the use of a normal distribution table, consider a scenario where a teacher wants to analyze the test scores of her students. Suppose the average score is 75 with a standard deviation of 10. If a student scores 85, the teacher can use the normal distribution table to find out how this score compares to the rest of the class. By calculating the Z-score, which is the number of standard deviations a particular score is from the mean, the teacher can convert the score into a Z-score using the formula: Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.In this case, the Z-score for a score of 85 would be calculated as follows: Z = (85 - 75) / 10 = 1. This means that a score of 85 is one standard deviation above the mean. The teacher can then look up this Z-score in the normal distribution table to find the corresponding percentile. For a Z-score of 1, the table indicates that approximately 84.13% of the scores lie below this value. Therefore, the teacher can conclude that the student scored better than approximately 84% of their peers.The normal distribution table is not only useful in academic settings but also in various fields such as psychology, finance, and quality control. In finance, for example, analysts use the table to assess risks and returns on investments. If an investment's return follows a normal distribution, analysts can predict the likelihood of achieving specific returns based on historical data. Similarly, in quality control, manufacturers can use the normal distribution table to determine the probability of defects in a production process, helping them maintain quality standards.In conclusion, the normal distribution table is an essential tool for anyone working with data. It provides valuable insights into the behavior of normally distributed variables and helps make informed decisions based on statistical evidence. By understanding how to utilize the normal distribution table, individuals can enhance their analytical skills and apply these concepts across various disciplines, from education to finance. As we continue to collect and analyze data in our increasingly data-driven world, mastering tools like the normal distribution table will remain integral to our success.

理解正态分布表的概念在统计学和数据分析中至关重要。正态分布表，也称为Z表，提供与标准正态分布相关的概率，标准正态分布是一个钟形曲线，表示许多类型数据的分布。这个表使统计学家能够确定一个值落在正态分布的某个范围内的可能性。正态分布由其均值和标准差定义。均值是数据集的平均值，而标准差则衡量数据点围绕均值的分散程度。当数据呈正态分布时，约68%的值落在均值的一标准差范围内，约95%落在两标准差范围内，约99.7%落在三标准差范围内。这个特性被称为经验法则或68-95-99.7法则。为了说明如何使用正态分布表，考虑一个场景：一位教师想要分析她学生的考试成绩。假设平均分为75，标准差为10。如果一名学生得了85分，教师可以使用正态分布表来找出这个分数与班级其他同学的比较。通过计算Z分数，即特定分数距离均值的标准差数量，教师可以使用公式Z = (X - μ) / σ将分数转换为Z分数，其中X是分数，μ是均值，σ是标准差。在这种情况下，85分的Z分数将如下计算：Z = (85 - 75) / 10 = 1。这意味着85分比均值高出一个标准差。然后，教师可以查阅正态分布表，找到对应的百分位数。对于Z分数为1，表明大约84.13%的分数低于这个值。因此，教师可以得出结论，该学生的成绩优于大约84%的同学。正态分布表不仅在学术环境中有用，还在心理学、金融和质量控制等多个领域中发挥作用。例如，在金融领域，分析师使用该表评估投资的风险和回报。如果投资的回报遵循正态分布，分析师可以根据历史数据预测实现特定回报的可能性。同样，在质量控制中，制造商可以利用正态分布表来确定生产过程中缺陷的概率，帮助他们维持质量标准。总之，正态分布表是任何处理数据的人必不可少的工具。它提供了关于正态分布变量行为的宝贵见解，并帮助基于统计证据做出明智的决策。通过理解如何利用正态分布表，个人可以增强他们的分析技能，并将这些概念应用于各个学科，从教育到金融。随着我们在越来越以数据驱动的世界中继续收集和分析数据，掌握像正态分布表这样的工具将始终是我们成功的关键。