# Normal Distribution v. Student's T Distribution

by kimberley
Tags: distribution, normal, student
 P: 14 The "Empirical Rule" states that if your data is normally distributed, 95.45% of that data should fall within "2" standard deviations of your Mean. There doesn't appear to be any reference to sample size in the literature regarding the Empirical Rule and a Normal Distribution. By contrast, however, the Student's T Distribution table, for a two-tailed test, has multipliers that differ from the Empirical Rule. Although where N=10000, at 9999 degrees of freedom, the .0455 level is "2" sd like the Empirical Rule, where N=20, at 19 degrees of freedom, the .0455 level is "2.14" sd. In sum, then, I don't understand the difference between the "normal distribution" and the "Student's T-Distribution". Is the difference that the Empirical Rule assumes that your data is both normal and "stationary" whereas the Student's T Distribution (i.e., degrees of freedom) assumes that your data is not stationary and that your Mean and Standard Deviations for any period of N will shift with the addition of new data? It's the only thing I can think of since the formulas for confidence intervals for Means and prediction intervals for individual outcomes use the numbers from the Student's T-Distribution. Thanks in advance. Kimberley
HW Helper