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The dynamical evolution of a tumor growth model, under immune surveillance and subject to non-Gaussian α-stable Levy noise, is explored. The lifetime of a tumor staying in the range between the tumor-free state and the stable tumor state, and the likelihood of noiseinducing tumor extinction, are characterized by the mean exit time (also called mean residence time) and the escape probability, respectively. For various initial densities of tumor cells, the mean exit time and the escape probability are computed with different noise parameters. It is observed that unlike the Gaussian noise, the non-Gaussian noise plays a constructive role in the tumor evolution in this simple model. By adjusting the noise parameters, the mean exit time can be shortened and the escape probability can be increased, simultaneously. This suggests that a tumor may be mitigated with higher probability in a shorter time, under certain external environmental stimuli.