What are the three standard deviations of the mean?

• A. 68% of values lie within 1 standard deviation of the mean; 95% within 2 standard deviations; 99.7% within 3 standard deviations
• B. 50%, 75%, 95%
• C. 60%, 90%, 99%
• D. 70%, 85%, 95%

Answer: (A)

This question hinges on the empirical rule for a normal distribution. It says that about 68% of observations fall within one standard deviation of the mean, about 95% fall within two standard deviations, and about 99.7% fall within three. Therefore the stated percentages—68% within one standard deviation, 95% within two, and 99.7% within three—match these bands around the mean, making this the correct description. The other percent patterns don’t align with the standard deviation spread of a normal curve, so they aren’t correct.