Approximately what range contains 99% of a population for a normally distributed trait?

Approximately what range contains 99% of a population for a normally distributed trait?

• A. Mean plus or minus 3 standard deviations
• B. Mean plus or minus 1 standard deviation
• C. Mean plus or minus 2 standard deviations
• D. The population mean

Answer: (A)

In a normal distribution, the spread of values around the mean follows the empirical rule: about 68% fall within one standard deviation, about 95% within two standard deviations, and about 99.7% within three standard deviations. So the range defined by the mean plus or minus three standard deviations encompasses essentially all the data—roughly 99% or more. That’s why it’s the best match for containing about 99% of the population. The other options describe narrower ranges: within one standard deviation captures only about 68%, within two standard deviations about 95%, and just the mean isn’t a range at all. If you wanted exactly 99%, you’d use about 2.58 standard deviations, but ±3 SD is the standard practical approximation.

In a normal distribution, the spread of values around the mean follows the empirical rule: about 68% fall within one standard deviation, about 95% within two standard deviations, and about 99.7% within three standard deviations. So the range defined by the mean plus or minus three standard deviations encompasses essentially all the data—roughly 99% or more. That’s why it’s the best match for containing about 99% of the population.

The other options describe narrower ranges: within one standard deviation captures only about 68%, within two standard deviations about 95%, and just the mean isn’t a range at all. If you wanted exactly 99%, you’d use about 2.58 standard deviations, but ±3 SD is the standard practical approximation.