Describing asymmetric first-order phase transitions by an order parameter distribution, there is a controversy in the literature concerning the relative normalization of the two occurring peaks. There are two rules for normalizing the distribution, called the “equal weight”-rule and the “equal height”-rule, which lead to different predictions of the finite-size scaling. We tested these predictions for an asymmetric model with two co-existing phases by means of a Monte Carlo simulation. We find overwhelming numerical evidence in favour of the “equal weight”-rule, showing at the same time that the shift of the susceptibility maximum with respect to the infinite volume transition point ht is proportional to L−2d, and not to L−d. In addition we tested a new method to determine the transition point ht which was recently proposed by Borgs and Janke.