In a normal distribution, what percentages lie within ±1σ, ±2σ, and ±3σ?

In a normal distribution, what percentages lie within ±1σ, ±2σ, and ±3σ?

• A. 34%, 68%, 95%
• B. 50%, 75%, 90%
• C. 68%, 95%, 99.7%
• D. 68%, 99%, 95%

Answer: (C)

Normal distributions follow a predictable pattern where data cluster near the mean and spread in standard deviations. The empirical rule says about 68% of values lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% lie within three standard deviations. So within ±1σ is roughly 68%, within ±2σ roughly 95%, and within ±3σ roughly 99.7% (exactly about 68.27%, 95.45%, and 99.73%). The other choices mix one-sided percentages or swap the two- and three-sigma values, which don’t align with the actual distribution.

Normal distributions follow a predictable pattern where data cluster near the mean and spread in standard deviations. The empirical rule says about 68% of values lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% lie within three standard deviations. So within ±1σ is roughly 68%, within ±2σ roughly 95%, and within ±3σ roughly 99.7% (exactly about 68.27%, 95.45%, and 99.73%). The other choices mix one-sided percentages or swap the two- and three-sigma values, which don’t align with the actual distribution.