Normal Curve and Z-Scores

The Normal Curve is otherwise known as the bell curve. It is a symmetric distribution centered about the mean and spread out by standard deviations. 68% of the data lies within the first standard deviation. 95% lies between the first two standard deviations. And 99.7% of the data falls within the first 3 standard deviations.  Anything outside of the first three standard deviations is considered an outlier of the data (which means that 0.3% of the observations will be outliers).

To calculate position on the Normal curve, we can use the z-score formula, which is the sample mean minus the population mean, all over the standard deviation. Our answer (the z-score) can be interpreted as the number of standard deviations (positive or negative) above or below the mean.