According to the empirical rule for a normal distribution, approximately what percentage lies within two standard deviations of the mean?

• A. About 68%
• B. About 75%
• C. About 99.7%
• D. About 95%

Answer: (D)

The empirical rule for the normal distribution describes how data are spread around the mean in terms of standard deviations. Roughly speaking, about 68% of observations fall within one standard deviation of the mean, about 95% fall within two standard deviations, and about 99.7% fall within three standard deviations. So, within two standard deviations from the mean, the proportion is about 95%. The remaining 5% lies outside that range, with roughly half in each tail beyond two standard deviations. This rule helps you gauge how concentrated data are around the mean and is a quick check for normal-shaped data.