The stochastic resonance (SR) phenomenon in human cognition (memory retrieval speed for arithmetical multiplication rules) is addressed in a behavioral and neurocomputational study. The results of an experiment in which performance was monitored for various magnitudes of acoustic noise are presented. The average response time was found to be minimal for some optimal noise level. Moreover, it was shown that the optimal noise level and the magnitude of the SR effect depend on the difficulty of the task. A computational framework based on leaky accumulators that integrate noisy information and provide the output upon reaching a threshold criterion is used to illustrate the observed phenomena.