Previous work on optimal allocation of work to production line systems has found that the throughput of a production line is maximized by deliberately unbalancing the line in an appropriate way when the processing time distribution is exponential or Erlang. A recent simulation study suggests that unbalancing the production line may not improve the efficiency of the line when the processing times are normally distributed. However, it appears that the unbalanced work allocation being studied may not be chosen appropriately in the simulation study and therefore, no significant improvement (and actually a decrease) in performance was observed when compared with the perfectly balanced work allocation. This study performs a similar set of simulation experiments of the previous study with normally distributed processing times, but uses more appropriate unbalanced work allocations to determine whether the efficiency of a production line can be improved if the line is unbalanced appropriately.