What type of distribution is characterized by a bell-shaped curve?

The type of distribution characterized by a bell-shaped curve is the normal distribution. This distribution is symmetric around the mean, which means that most of the data points cluster around the average, with fewer occurrences as you move away from the mean in either direction. The shape is defined precisely by the properties of the mean and standard deviation, highlighting how data is distributed around a central point.

In practical terms, a normal distribution is prevalent in many natural phenomena, such as heights, test scores, and measurement errors, where the majority of data falls within a certain range, tapering off as you move farther from the mean. The bell shape reflects this concentration of data points and provides a useful model for various statistical analyses, including hypothesis testing and confidence intervals.

The other distributions listed do not share this bell-shaped characteristic. For example, uniform distribution has a constant probability across a range of values, while exponential distribution is used to model time until an event occurs, like decay processes, and does not have the symmetry or bell shape. Binomial distribution represents the number of successes in a fixed number of independent Bernoulli trials and typically forms a different shape depending on the probabilities of success and failure within those trials.