A one-dimensional lattice percolation model is constructed for the bond problem at flowing along non-nearest neighbors. Arbitrary parameters were taken (percolation radius, number of nodes in a one-dimensional lattice and number of experiments). Based on original algorithms operating on a computer faster than standard ones, the values of the percolation threshold were obtained with the corresponding error. Based on these data, the hypothesis about the normal distribution of the percolation threshold is tested. Using Pearson’s criterion it was shown for the first time that there is no reason to reject this hypothesis for one-dimensional problems of bonds and sites with an arbitrary percolation radius.