What type of distribution is characterized by being symmetrical about the mean, forming a bell-shaped curve?

The type of distribution characterized by being symmetrical about the mean and forming a bell-shaped curve is the normal distribution. This distribution is significant in statistics because many natural phenomena tend to follow this pattern, such as heights, test scores, and measurement errors.

In a normal distribution, the mean, median, and mode are all located at the center of the distribution, which means the data points are evenly distributed on either side of the mean. The bell shape indicates that values closer to the mean are more frequent, while extreme values are less common. This shape arises from the properties of many independent random variables that combine, leading to the central limit theorem, which states that, under certain conditions, the sum of many independent random variables will tend toward a normal distribution, regardless of the original distribution of the variables.

Other distributions mentioned, such as exponential distribution, do not exhibit symmetry and have specific applications related to time until an event occurs. A biased distribution would signify a lack of symmetry or a preference for certain outcomes, while a uniform distribution indicates that every outcome is equally likely and does not resemble a bell shape.