Earlier forms for the coherent reflection and incoherent scattering by multicomponent mixtures of bosses on rigid or free base planes [V. Twersky, J. Acoust. Soc. Am.29, 209–225 (1957)] are applied to recent high‐frequency results for aligned hemiellipsoidal bosses [R. J. Lucas and V. Twersky, J. Acoust. Soc. Am.83, 2005–2011 (1988)] to investigate continuous distributions in boss size. Approximations for the coherent reflected intensity and incoherent differential scattering cross sections are obtained in terms of integrals of simple functions and a general probability density. To provide illustrations, numerical computations and graphical results are based on truncating the two‐parameter gamma probability density functionP(t;m,v) withtas a dimensionless variable that scales one or more boss dimensions,mas the mean value oft, andvas the normalized variance (ranging from zero to unity). Forvsmall,Pis Gaussian and reduces to a delta function asvapproaches zero (to reproduce one‐component results). More generally, the curve ofPis skewed, and asvapproaches unityPreduces to the exponential for the simplest Poisson case. Graphs are shown for cases where one (e.g., keel depth), two (e.g., base axes), or all three dimensions of the protuberances are randomized. The essentials are indicated by plots versus angle of incidence, withvas the parameter. The coherent intensity and the associated forward and backscattered incoherent differential scattering cross sections per unit area are emphasized.