In this letter, we investigate the non-orthogonal multiple access (NOMA) assisted mobile edge computing (MEC) system, where multiple tasks with heterogeneous latency requirements are offloaded simultaneously. In particular, previous works assumed that the task streams are transmitted un-intermittently for simplicity, which resulted in suboptimal performance. To address this problem, an energy-efficient rate allocation scheme is proposed when only statistical channel state information (CSI) is available. And the energy minimization problem under latency and outage constraints is formulated. Then the optimal SIC order is obtained and an iterative water-filling (IWF)-based rate allocation algorithm is developed to solve this problem. Numerical results indicate that the proposed scheme improves the energy efficiency.