In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

• A. 95.4%
• B. 50%
• C. 68.3%
• D. 99.8%

Answer: (C)

The main idea tested is the empirical rule for a normal distribution: about 68% of observations lie within one standard deviation of the mean. Because the normal curve is symmetric and the standard deviation defines the spread, the interval from μ − σ to μ + σ corresponds to the area between z = −1 and z = +1. That central area amounts to about 0.6827 of the total area, i.e., 68.27%, typically rounded to 68.3%. For context, roughly 95.4% fall within two standard deviations and about 99.7% within three standard deviations, which explains why the other options correspond to larger spans. So the figure that matches the one-standard-deviation interval is 68.3%.

The main idea tested is the empirical rule for a normal distribution: about 68% of observations lie within one standard deviation of the mean. Because the normal curve is symmetric and the standard deviation defines the spread, the interval from μ − σ to μ + σ corresponds to the area between z = −1 and z = +1. That central area amounts to about 0.6827 of the total area, i.e., 68.27%, typically rounded to 68.3%. For context, roughly 95.4% fall within two standard deviations and about 99.7% within three standard deviations, which explains why the other options correspond to larger spans. So the figure that matches the one-standard-deviation interval is 68.3%.