For a normal distribution, which of the following statements is true about the $\mathrm{mean}$, $\mathrm{median}$, and $\mathrm{mode}$?

• A. The $\mathrm{median}$ is always greater than the $\mathrm{mode}$.
• B. The $\mathrm{mean}$ is always greater than the $\mathrm{median}$.
• C. The $\mathrm{mode}$ is always less than the $\mathrm{mean}$.
• D. The $\mathrm{mean}$, $\mathrm{median}$, and $\mathrm{mode}$ are all equal.

Answer: (D)

Verified step by step guidance

1. Recall the properties of a normal distribution, which is symmetric and bell-shaped.
2. Understand that in a perfectly normal distribution, the mean, median, and mode coincide at the center of the distribution.
3. Recognize that because of this symmetry, the mean, median, and mode have the same value.
4. Evaluate each statement by comparing the relative positions of mean, median, and mode in a normal distribution.
5. Conclude that the only true statement is that the mean, median, and mode are all equal in a normal distribution.