Approximately what percent of the norming group in a normal distribution falls between two standard deviations below the mean and two standard deviations above the mean?

Approximately what percent of the norming group in a normal distribution falls between two standard deviations below the mean and two standard deviations above the mean?

• A. 68%
• B. 95%
• C. 99.7%
• D. 50%

Answer: (B)

Think of the empirical rule for a normal distribution. It describes how data cluster around the mean in terms of standard deviations: about 68% fall within one standard deviation, about 95% fall within two standard deviations, and about 99.7% fall within three. So the portion between two standard deviations below the mean and two above encompasses about 95% of the distribution. The precise figure is roughly 95.4%, since the tails beyond ±2σ together account for about 5% of the data. This interval is larger than the one-standard-deviation range (68%) but smaller than the three-standard-deviation range (99.7%). In short, this interval captures most of the norming group—about 95%.

Think of the empirical rule for a normal distribution. It describes how data cluster around the mean in terms of standard deviations: about 68% fall within one standard deviation, about 95% fall within two standard deviations, and about 99.7% fall within three.

So the portion between two standard deviations below the mean and two above encompasses about 95% of the distribution. The precise figure is roughly 95.4%, since the tails beyond ±2σ together account for about 5% of the data. This interval is larger than the one-standard-deviation range (68%) but smaller than the three-standard-deviation range (99.7%).

In short, this interval captures most of the norming group—about 95%.