Final answer:
The question seeks to identify an interval with a local minimum of 0 from a graph, but no actual graph is provided. Without a specific graph, the interval with a local minimum of 0 cannot be determined. Descriptions of a horizontal line and various distributions do not provide enough context to find a local minimum.
Step-by-step explanation:
The question refers to identifying the interval on the graph of a function that has a local minimum of 0. However, the provided information does not include a specific graph to refer to, but it does indicate a range for the variable x and describes the characteristics of some functions and distributions. A local minimum is a point on a graph where the function's value is lower than at points immediately to its left and right. Given the absent graph, we cannot definitively determine the interval with a local minimum of 0. Nevertheless, a horizontal line, as described, does not have local minima or maxima because its derivative (rate of change) is zero everywhere, and its function value is constant.
Common types of distributions mentioned, such as the uniform distribution and the exponential distribution, have specific properties and probabilities associated with intervals within their range. However, without a specific graph or additional context, the interval with a local minimum of 0 cannot be determined.