What type of distribution does the Empirical Rule require to apply?

The Empirical Rule, often referred to as the 68-95-99.7 rule, specifically applies to normal distributions. This statistical principle states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and around 99.7% falls within three standard deviations. This characteristic makes the normal distribution a key concept in probability and statistics, particularly for understanding data variability and the tendency of data points around the mean.

In contrast, other types of distributions like uniform or binomial distributions do not exhibit the same properties of symmetry and defined percentages around the mean. For instance, a uniform distribution spreads values evenly across a range, while a binomial distribution focuses on the number of successes in a fixed number of independent trials. An exponential distribution models the time until an event occurs and is also not aligned with the symmetrical attributes of the normal distribution. Therefore, the Empirical Rule is exclusively applicable to data that follows a normal distribution.