A method and associated systems for a resource-utilization monitor with self-adjusting sample size. A processor monitors availability of a resource-limited entity by analyzing a set of samples that each identify, at the time the sample was recorded, an unused amount of resource available to the entity. The processor computes a Chi-square statistic of the sample set. If the statistic reveals that the number of samples in the sample set is too small to produce valid results, the processor adjusts the sample size to specify a larger number of samples and repeats these steps. If the number of samples is large enough to produce statistically valid results, the processor analyzes the sample set to determine whether the current amount of remaining resource is undesirably low, is likely to become undesirably low during a short-term period of time, or is likely to become undesirably low during a longer-term period of time.