What is the shape of a normal distribution?

A normal distribution is characterized by its bell-shaped curve, which is symmetric around the mean. This symmetry means that the left and right halves of the distribution are mirror images of each other. In a normal distribution, most of the data points cluster around the mean, with fewer points occurring as you move away from the mean in either direction. This results in the classic bell shape, where the highest point occurs at the mean, and the tails extend indefinitely, although they approach, but never actually reach, the horizontal axis.

This shape is important in statistics because it helps illustrate key concepts such as the empirical rule, which states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. This characteristic of the normal distribution plays a crucial role in inferential statistics, hypothesis testing, and various other applications in data analysis.