The Li7 NMR spin-lattice relaxation and the electrical conductivity in the typical glassy fast-ion conductor (Li2S)0.56(SiS2)0.44 are discussed from models of Li+ionic motion with distributions of activation energies, as well as from stretched-exponential time-correlation functions. The measured correlation times from the two effects differ by two orders of magnitude, and the derived distributions are shifted greatly relative to each other. We relate the great differences to percolation around the high barriers in the distribution. We present a phenomenological theory that yields good quantitative fits to the observed NMR relaxation with a Gaussian distribution, and to the conductivity and related dielectric properties with the continuous-time random-walk model and the same Gaussian truncated at the percolation limit. This correlates the two effects in a simple and effective way; both time-correlation functions can be calculated approximately from the distributions, and even the dc conductivity can be calculated from the NMR results. The present approach is discussed and compared with previously proposed models to explain the anomalies in ac electrical-conductivity and NMR relaxation rates in glassy fast-ion conductors.