The empirical rule states that in a normal distribution, what percentage of observations lie within two standard deviations of the mean?

• A. 68%
• B. 50%
• C. 95%
• D. 99%

Answer: (C)

In a normal distribution, data follow the empirical rule, often called the 68-95-99.7 rule. This rule tells us how data cluster around the mean in terms of standard deviations. About 68% lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% lie within three standard deviations. Therefore, within two standard deviations of the mean, roughly 95% of observations fall. The other options correspond to different ranges: 68% is for one standard deviation, 50% isn’t a standard bracket in this rule, and 99% isn’t the usual figure—it's about 99.7% within three standard deviations.