In a normal distribution, which statement correctly describes the proportion of outcomes that lie beyond two standard deviations from the mean?

In a normal distribution, which statement correctly describes the proportion of outcomes that lie beyond two standard deviations from the mean?

• A. Between one and two standard deviations above or below the mean.
• B. Within one standard deviation above or below the mean.
• C. Outside two standard deviations above or below the mean.
• D. Between the mean and two standard deviations above or below the mean.

Answer: (C)

In a normal distribution, the empirical rule tells us how data spread around the mean: about 68% fall within one standard deviation, about 95% within two standard deviations, and about 99.7% within three. That means the outcomes beyond two standard deviations from the mean—the tails on either side—make up the remaining portion, roughly 5% in total (about 2.5% in each tail). So the statement describing outcomes outside two standard deviations correctly captures the tail regions far from the mean. The other descriptions refer to regions inside or closer to the mean, which do not match the idea of outcomes beyond two standard deviations.

In a normal distribution, the empirical rule tells us how data spread around the mean: about 68% fall within one standard deviation, about 95% within two standard deviations, and about 99.7% within three. That means the outcomes beyond two standard deviations from the mean—the tails on either side—make up the remaining portion, roughly 5% in total (about 2.5% in each tail). So the statement describing outcomes outside two standard deviations correctly captures the tail regions far from the mean. The other descriptions refer to regions inside or closer to the mean, which do not match the idea of outcomes beyond two standard deviations.