In a normal distribution, what percentage lies within two standard deviations of the mean?

In a normal distribution, what percentage lies within two standard deviations of the mean?

• A. 68.3%
• B. 99.8%
• C. 75%
• D. 95.4%

Answer: (D)

In a normal distribution, the data within two standard deviations of the mean cover most of the distribution—about 95.4% of observations. This comes from the empirical rule for normal distributions: roughly 68% fall within one standard deviation, about 95% within two, and about 99.7% within three. The exact value is 2Φ(2) − 1 ≈ 0.9545, i.e., 95.45%, so the closest stated percentage is 95.4%. The other options correspond to the one-sigma interval (68.3%), a rough three-sigma approximation (around 99.7%), or an outlier value (75%), which is not the two-standard-deviation interval.

In a normal distribution, the data within two standard deviations of the mean cover most of the distribution—about 95.4% of observations. This comes from the empirical rule for normal distributions: roughly 68% fall within one standard deviation, about 95% within two, and about 99.7% within three. The exact value is 2Φ(2) − 1 ≈ 0.9545, i.e., 95.45%, so the closest stated percentage is 95.4%. The other options correspond to the one-sigma interval (68.3%), a rough three-sigma approximation (around 99.7%), or an outlier value (75%), which is not the two-standard-deviation interval.