Due to gradual disappearance of global demographic dividend, the improvement of workforce efficiency becomes increasingly important. It has been commonly recognised that workforce motivation can largely stimulate the workers, especially in manufacturing systems. This paper investigates a worker scheduling problem under given work shifts with workforce motivation effects, where motivation effects are characterised by motivation coefficients of job processing times. We focus on the situation where motivation coefficients are uncertain due to various factors, and only the mean vector and covariance matrix are known. The objective is to maximise the service level, measured by the probability of ensuring no tardy jobs. We first propose a distributionally robust chance constrained formulation with a probabilistic objective function. Then an adapted sample average approximation (SAA) method and a heuristic, based on an approximated mixed integer second-order cone programming (MI-SOCP) model and the idea of problem decomposition, is developed. Numerical results show that the decomposition-based heuristic is more efficient. We also draw some managerial insights.