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Rigorous verification of neural nets is necessary in safety-critical applications such as commercial aviation. This paper investigates feasibility of a randomized approach to the problem. The previously developed deterministic verification method suffers from exponential growth of computational complexity as a function of problem dimensionality, which limits its applicability to low dimensional cases. In contrast, complexity of the randomized method is independent from the problem dimension. Verification of a neural net is formulated as Monte Carlo estimation of probability of failure. The required number of random samples is analyzed. Instead of the general Chernov-based bound, a significantly improved condition is found by exploiting the special case when the number of observed failures is zero. It is shown that with the currently available computers the method is a viable alternative to the deterministic technique. Issues regarding possible acceptance of statistical verification by certification authorities are also, briefly discussed.