The normal distribution is a theoretical distribution of values. It is often called the bell curve because the visual representation of this distribution resembles the shape of a bell. It is theoretical because its frequency distribution is derived from a formula rather than the observation of actual data.
Even though the normal distribution is theoretical, the distributions of many fields in the real world resemble the normal distribution. An example is the traditional bell curve for ranking students. Most students have average grades (the mean), while there are a few with the poorest grades and a few with the highest grades.
The assumption of normality is important for many statistical tests. If the shape of a field’s distribution is not bell-shaped, some statistical tests might not be valid.
The normal distribution is symmetric about the mean. That is, the distributions of values to the right and left of the mean are mirror images. 68% of the values in the distribution fall within one standard deviation of the mean (to the left and right). 95% of values fall within two standard deviations, and 99.7% within three.