Approximately what range contains 95% of a population for a normally distributed trait?

Approximately what range contains 95% of a population for a normally distributed trait?

• A. Mean plus or minus 1 standard deviation
• B. Mean plus or minus 3 standard deviations
• C. Mean plus or minus 2 standard deviations
• D. All observed values within the population

Answer: (C)

In a normal distribution, the spread around the mean is captured by the standard deviation, and the empirical rule describes how data fall within certain multiples of that spread. About 68% lie within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three. So, approximately 95% of observations fall between the mean minus two standard deviations and the mean plus two standard deviations. If you want the exact 95% bound, it’s actually between -1.96 and +1.96 standard deviations, but using two standard deviations is the common practical approximation. The other options correspond to different percentages (±1 SD gives ~68%, ±3 SD gives ~99.7%) or are not consistent with a finite, all-observed-values range.

In a normal distribution, the spread around the mean is captured by the standard deviation, and the empirical rule describes how data fall within certain multiples of that spread. About 68% lie within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three.

So, approximately 95% of observations fall between the mean minus two standard deviations and the mean plus two standard deviations. If you want the exact 95% bound, it’s actually between -1.96 and +1.96 standard deviations, but using two standard deviations is the common practical approximation. The other options correspond to different percentages (±1 SD gives ~68%, ±3 SD gives ~99.7%) or are not consistent with a finite, all-observed-values range.