An analysis of the bottom baryon decay Λb→J/ψ(→μ+μ-)Λ(→pπ-) is performed to measure the Λb polarization and three angular parameters in data from pp collisions at s=7 and 8 TeV, collected by the CMS experiment at the Large Hadron Collider. The Λb polarization is measured to be 0.00±0.06(stat)±0.06(syst) and the parity-violating asymmetry parameter is determined to be 0.14±0.14(stat)±0.10(syst). The measurements are compared to various theoretical predictions, including those from perturbative quantum chromodynamics.