The Kepler Mission has found thousands of planetary candidates with radii between 1 and 4R_{Earth}_. These planets have no analogues in our own solar system, providing an unprecedented opportunity to understand the range and distribution of planetary compositions allowed by planet formation and evolution. A precise mass measurement is usually required to constrain the possible composition of an individual super-Earth-sized planet, but these measurements are difficult and expensive to make for the majority of Kepler planet candidates (PCs). Fortunately, adopting a statistical approach helps us to address this question without them. In particular, we apply hierarchical Bayesian modeling to a subsample of Kepler PCs that is complete for P<25 days and R_pl_>1.2R_{Earth}_ and draw upon interior structure models that yield radii largely independent of mass by accounting for the thermal evolution of a gaseous envelope around a rocky core. Assuming the envelope is dominated by hydrogen and helium, we present the current-day composition distribution of the sub-Neptune-sized planet population and find that H+He envelopes are most likely to be ~1% of these planets' total masses with an intrinsic scatter of +/-0.5 dex. We address the gaseous/rocky transition and illustrate how our results do not result in a one-to-one relationship between mass and radius for this sub-Neptune population; accordingly, dynamical studies that wish to use Kepler data must adopt a probabilistic approach to accurately represent the range of possible masses at a given radius.