In this letter, we model the downstream bit rate per user for VDSL2-based access systems as normal random variable. Its statistics are expressed in closed analytic forms explicitly accounting for FEXT fluctuation and for the access network geometry. The considered approximation is obtained assuming log-normal statistics for the signal-to-interference plus noise ratio per sub-carrier. The validity of this model has been assessed by computer calculation showing a very good agreement between the exact and the approximated bit rates