Answer :
Final answer:
The Empirical Rule, or 68-95-99.7 rule, is a statistical guideline stating that for a normal distribution approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Explanation:
The Empirical Rule, often referred to as the 68-95-99.7 rule or the three-sigma rule, is an essential concept in statistics relating to the distribution of data within a normal distribution, which is bell-shaped and symmetric.
According to this rule, about 68 percent of the data falls within one standard deviation (σ) of the mean (μ), about 95 percent of the data falls within two standard deviations, and about 99.7 percent of the data falls within three standard deviations.
In terms of z-scores, this translates to approximately 68 percent of data values lying between z-scores of -1 and 1, about 95 percent between z-scores of -2 and 2, and about 99.7 percent between z-scores of -3 and 3. This rule is particularly useful in various aspects of data analysis, including understanding the distribution of sample means and setting up confidence intervals.
