Human neural progenitor cells (hNPCs) form a new prospect for replacement therapies in the context of neurodegenerative diseases. The Wnt/β-catenin signaling pathway is known to be involved in the differentiation process of hNPCs. In this paper, we present a computational modeling study on the dynamics of the Wnt/β-catenin signaling pathway in RVM cells, a common cell model of hNPCs. A concern when investigating RVM cells in vitro is that experimental results are possibly biased by the asynchrony of cell w.r.t. the cell cycle. To this end, we present a model of RVM cell populations that combines the Wnt/β-catenin signaling pathway with cell cycle control. Thereby, the model of the pathway in single cells is inspired by, extends on, and is validated by comparing to the reference model in literature. We present a study on the population model that compares simulation results to our own wet-lab data, obtained by Western-blot experiments. It starts with a stochastic investigation that reveals strong fluctuations in the dynamics of the pathway that directly result from model parameters provided in literature and that are not observable in deterministic investigations. These let us conclude that crucial mechanisms of noise reduction in the Wnt/β-catenin signaling pathway may still be unknown. We provide a new parameter set that is obtained by parameter fitting experiments and provides only insignificant fluctuations. Based on this, we present results that show that in in vitro experiments the impact of the cell cycle can be neglected. The results also suggest that in RVM cells a self-induced Wnt signal possibly occurs. We underline this point by a small extension of our model. Furthermore, we propose a couple of experimental set-ups to further investigate self-induced Wnt signaling in RVM cells, by this closing the cycle of computational systems biology.