The probability distribution for biomass of many marine species varies in space, partly as a function of bottom depth. A non-parametric method is described for using trawl survey data to estimate the probability distribution at any point in the survey region whose bottom depth is known. Integrating the expected value of the distribution over the region provides an estimate of the biomass in the region. Repeated sampling from the estimated distributions at the survey points enables us to compute a Monte Carlo confidence interval for the biomass. For two surveys of northern shrimp in NAFO Div. 2HJ, these methods produced confidence intervals that are narrower than those computed using methods based on stratified-random sampling and an assumed Gaussian distribution.