Arizona State University (ASU) STP226 Elements of Statistics Exam 1 Practice

The empirical rule, also known as the 68-95-99.7 rule, is a statistical principle that applies to data that is normally distributed. It provides a way to understand the distribution of data points in relation to the mean and standard deviations.

In the context of this rule, approximately 68% of the data falls within one standard deviation from the mean, about 95% falls within two standard deviations, and around 99.7% of the data is captured within three standard deviations from the mean. This encompasses the range within which most of the data points are likely to lie in a normal distribution.

The choice that identifies three standard deviations encompassing 99.7% of the data accurately reflects this principle of the empirical rule. Understanding this rule is essential as it helps statisticians and data analysts make inferences about a population based on a sample, as well as assessing how extreme or typical certain data points might be.