In a normal distribution, which set lists the correct percentages within one, two, and three standard deviations?

In a normal distribution, which set lists the correct percentages within one, two, and three standard deviations?

• A. 50%, 50%, 50%
• B. 90%, 95%, 99%
• C. 68%, 95%, 99.7%
• D. 60%, 95%, 99%

Answer: (C)

In a normal distribution, the empirical rule describes how data cluster around the mean: about 68% lie within one standard deviation, about 95% within two, and about 99.7% within three. This pattern is a hallmark of the normal curve and is used to estimate probabilities from standard deviations. The option that lists 68%, 95%, 99.7% matches this rule exactly, so it’s the best choice. The other options misstate the amount within one standard deviation (it’s not 50%, 60%, or 90%), even though their two- and three-standard-deviation values may look similar.

In a normal distribution, the empirical rule describes how data cluster around the mean: about 68% lie within one standard deviation, about 95% within two, and about 99.7% within three. This pattern is a hallmark of the normal curve and is used to estimate probabilities from standard deviations.

The option that lists 68%, 95%, 99.7% matches this rule exactly, so it’s the best choice. The other options misstate the amount within one standard deviation (it’s not 50%, 60%, or 90%), even though their two- and three-standard-deviation values may look similar.