What statistical rule is associated with the normal distribution?

The Empirical Rule is indeed closely associated with the normal distribution. This rule states that for a bell-shaped distribution, approximately 68% of the data points fall within one standard deviation of the mean, about 95% are within two standard deviations, and around 99.7% lie within three standard deviations. This provides a simple way to understand the dispersion and spread of data within a normal distribution.

Using the Empirical Rule helps to visualize how data is distributed around the mean and allows for quick estimation of probabilities for a normally distributed variable. It is particularly useful in statistics for making inferences about populations based on sample data within the context of the normal distribution, which is fundamental in various statistical analyses.

The Central Limit Theorem, while important, relates to the distribution of sample means and states that, given a sufficiently large sample size, the sampling distribution of the sample mean will be normally distributed regardless of the original distribution's shape. The Law of Large Numbers pertains to the property that as the number of trials in an experiment increases, the sample mean will get closer to the expected value. Regression analysis involves modeling the relationship between variables, which does not directly address the characteristics of the normal distribution itself.