Hospitals commonly project demand for their services by combining their historical share of regional demand with forecasts of total regional demand . Hospital-specific forecasts of demand that provide prediction intervals, rather than point estimates, may facilitate better managerial decisions, especially when demand overage and underage are associated with high, asymmetric costs . Regional point forecasts of patient demand are commonly available, e.g., for the number of people requiring hospitalization due to an epidemic such as COVID-19 . However, even in this common setting, no probabilistic, consistent, computationally tractable forecast is available for the fraction of patients in a region that a particular institution should expect . We introduce such a forecast, DICE (Demand Intervals from Consistent Estimators). We describe its development and deployment at an academic medical center in California during the 'second wave' of COVID-19 in the Unite States . We show that DICE is consistent under mild assumptions and suitable for use with perfect, biased and unbiased regional forecasts . We evaluate its performance on empirical data from a large academic medical center as well as on synthetic data.