Approximately what percentage of the area under the normal curve lies within plus or minus three standard deviations from the mean?

• A. 99.73%
• B. 68.27%
• C. 95.45%
• D. 99.0%

Answer: (A)

This question tests the normal distribution and the empirical rule, which describes how much of the data lies within a given number of standard deviations from the mean. For a normal curve, about 68.27% lies within ±1 standard deviation, about 95.45% within ±2 standard deviations, and about 99.73% within ±3 standard deviations. So the area between -3 and +3 standard deviations is approximately 99.73%. The remaining 0.27% lies beyond ±3σ, split roughly 0.135% in each tail. That’s why 99.73% is the best answer. The other numbers match the smaller ranges (within ±1 or ±2 SD) or a rounded figure, but not the exact 3-sigma interval.