Which distribution is characterized by having a distinct bell-shaped curve?

The normal distribution is recognized for its distinct bell-shaped curve, which is symmetric around the mean. This curve represents the distribution of data where most of the values cluster around the central peak, with probabilities tapering off equally in both directions away from the mean.

In a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% lies within two standard deviations, and around 99.7% is within three standard deviations. This characteristic makes the normal distribution extremely important in statistics, particularly due to the Central Limit Theorem, which states that the sum of a large number of independent, identically distributed variables will tend toward a normal distribution, regardless of the original distributions of the variables.

The other distributions do not exhibit this bell-shaped symmetry. For instance, a uniform distribution has equal probability across its range and appears as a flat, even line rather than a curve. An exponential distribution is often used to model time until an event occurs and typically has a rapid decrease. A skewed distribution lacks symmetry and leans towards one side, resulting in a longer tail on one end. Thus, the normal distribution is distinct and foundational in statistics for its bell shape and its critical role in statistical theory and practice