What type of distribution has constant probability across an interval?

A uniform distribution is characterized by having a constant probability across its defined interval. This means that every outcome within that interval is equally likely to occur. In graphical terms, a uniform distribution appears as a flat, horizontal line over the interval, indicating that the probability density function is constant.

For example, if you have a uniform distribution over the interval from 0 to 1, every value within that range has the same probability density, which reflects the equal likelihood of occurrence.

In contrast, other distributions do not maintain this constant probability across their ranges. The normal distribution is characterized by a bell-shaped curve, where probabilities vary with distance from the mean—higher near the center and decreasing towards the tails. The binomial distribution relates to scenarios of a fixed number of trials with two possible outcomes (success or failure), and its probabilities depend on the number of successes and the probability of success in individual trials. The geometric distribution models the number of trials required to achieve one success, creating a decreasing probability related to the trials involved.

Thus, the defining feature of the uniform distribution as having constant probability across an interval is the reason it stands out as the correct choice.