Data Analysis with R, Second Edition - Second Edition

The three-sigma rule and using z-tables

When dealing with a normal distribution, we know that it is more likely to observe an outcome that is close to the mean than it is to observe one that is distant—but just how much more likely? Well, it turns out that roughly 68% of all the values drawn from a random distribution lie within one standard deviation, or one z-score, away from the mean. Expanding our boundaries, we find that roughly 95% of all values are within two z-scores from the mean. Finally, about 99.7% of normal deviates are within three standard deviations from the mean. This is called the three-sigma rule.

Figure 4.6: The three-sigma ...