What characterizes the normal distribution?

The normal distribution is characterized by its symmetric shape around the mean, which forms a bell curve. This means that the data points are evenly distributed on either side of the mean, with the majority of the observations clustering around the center and fewer observations appearing as you move away from the center in either direction. This symmetry is a key feature, making the normal distribution an important concept in statistics, particularly in inferential statistics where properties like the central limit theorem apply.

The shape of the normal distribution leads to predictable probabilities for standard deviations from the mean. Approximately 68% of data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations. This makes it incredibly useful for statistical analysis and hypothesis testing. The characteristic bell curve implies that extreme values (outliers) are unlikely, contributing to the normality assumption in many statistical methods.