We revisit the one-dimensional stochastic model of an earlier study by D. K. Lubensky and D. R. Nelson for the electrically driven translocation of polynucleotides through alpha-hemolysin pores. We show that the model correctly describes two further important properties of the experimentally observed translocation time distributions, namely their spread (width) and their exponential The resulting overall agreement between theoretical and experimental translocation time distributions is thus very good.