In a normal distribution, which statement is true?

• A. No outliers in a normal distribution
• B. The distribution is heavily skewed
• C. Mean is always greater than the median
• D. About 68% lie within one standard deviation of the mean

Answer: (D)

Normal distributions are symmetric around the mean, with the spread set by the standard deviation, so the mean, median, and mode coincide. A fundamental result is the 68-95-99.7 rule: about 68% of observations fall within one standard deviation of the mean, about 95% within two, and about 99.7% within three. This makes the statement that about 68% lie within one standard deviation true. The distribution is not heavily skewed, so the mean is not greater than the median—indeed, they are equal in a normal curve. Also, the tails go on forever, so there can be values far from the center, meaning there can be outliers in practice, not a scenario with none.