Which of the following is a characteristic of a normal distribution?

A normal distribution is characterized by its symmetry around the mean, meaning that the left half of the distribution is a mirror image of the right half. This symmetry indicates that the mean, median, and mode of the distribution are all located at the same central point.

This characteristic is crucial because it implies that data points are equally likely to occur on either side of the mean, and as a result, most values lie closer to the mean, with frequencies tapering off symmetrically as one moves away from the center. This property is fundamental to many statistical methods and analyses, as it simplifies calculations and predictions regarding data sets that approximate a normal distribution.

In contrast, a distribution that is skewed to the right would show a longer tail on the right side and would not be symmetric. A distribution with two peaks is known as bimodal, which deviates from the single-peaked nature of a normal distribution. Having infinite variance is not a feature of a normal distribution; instead, it has a finite variance that determines its spread. Therefore, symmetry around the mean is the defining characteristic to identify a normal distribution accurately.