What is a characteristic of a normal distribution?

A normal distribution is a key concept in statistics characterized primarily by its symmetry about the mean. This means that if you were to draw the probability density function, the left side of the distribution would mirror the right side. In a normal distribution, the mean, median, and mode all coincide at the center of the distribution, indicating that the data is evenly distributed around that central value.

The property of symmetry is significant as it implies that there is an equal likelihood of values occurring above and below the mean. This characteristic also leads to the tails of the distribution tapering off equally in both directions. Such symmetry is fundamental to many statistical methods, including hypothesis testing and confidence interval estimation.

The incorrect choices reflect common misunderstandings of distribution shapes. For example, if a distribution is skewed to the left, it means that the left tail is longer or fatter than the right, which contradicts the definition of a normal distribution. Similarly, a normal distribution has a single peak (or mode), and it does not contain multiple modes, as that would define a multimodal distribution. While data in a normal distribution does indeed become less frequent as it moves away from the mean, this is more of an observation about the tails rather than a defining characteristic of the normal