The density of states for a tight-binding electron in disordered coupled chains with a weak Gaussian diagonal randomness is simulated using Dean's method under various magnetic fields. These data are compared with the results of the coherent-potential approximation (CPA) based on the analytic Green function obtained recently by the present authors. The CPA is shown to give quantitatively good results except in the near-tail regions. The scaling behaviour near the band edges (including the near-tail regions) are also examined in detail. It is found that, when the magnetic field is above a critical field scaling exists and follows the one-dimensional universal function. Below this critical field, a non-universal energy shift is required before scaling can apply. The existence of this energy shift also limits the range of scaling to a smaller randomness.