Empirical Rule vs Normal Distribution
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Empirical rule
Random variables and distributions
The empirical rule says that in a normal distribution, about 68, 95, and 99.7 percent of values fall within 1, 2, and 3 standard deviations of the mean.
The empirical rule, also called the 68-95-99.7 rule, describes how data cluster in a normal distribution. About 68 percent of values fall within 1 standard deviation of the mean, about 95 percent within 2, and about 99.7 percent within 3. For example, if adult heights are normal with mean 68 inches and standard deviation 3 inches, about 95 percent fall between and inches. It gives quick estimates without needing a z-table.
Normal distribution
Random variables and distributions
The normal distribution is a symmetric, bell-shaped density curve described by its mean and standard deviation.
The normal distribution is a bell-shaped curve centered at its mean (mu) and spread out by its standard deviation (sigma). Many natural measurements, such as heights or measurement errors, are approximately normal. For example, adult heights cluster near an average, with fewer people far above or below it. The empirical rule says about 68, 95, and 99.7 percent of the data fall within 1, 2, and 3 standard deviations of the mean.