What percent of the population is within +/- 1, 2, and 3 standard deviations in a normal distribution?

• A. 68.27%, 95.45%, 99.73%
• B. 50%, 75%, 95%
• C. 34%, 68%, 95%
• D. 60%, 90%, 99%

Answer: (A)

The idea here is the empirical rule for a normal distribution: most values cluster around the mean, and specific fractions fall within 1, 2, and 3 standard deviations.

Within one standard deviation of the mean, about 68.27% of observations fall inside. This comes from the symmetry of the normal curve and the area under the curve between -1 and +1 standard deviation. The tails beyond ±1 SD together contain about 31.73%, leaving 68.27% in the middle.

Within two standard deviations, about 95.45% fall inside. Beyond ±2 SD, only about 4.55% remain, split between the two tails.

Within three standard deviations, about 99.73% fall inside. Only about 0.27% lie beyond ±3 SD.

So the set 68.27%, 95.45%, 99.73% matches these well-established percentages.

The other options mix up these proportions, either giving the wrong value for the inside of one SD or misaligning the two- and three-SD ranges.