A variation of the three-parameter two-sided power distribution is presented as a linear combination of bivariate Dirichlet. In this variant of the distribution, referred to as the N DS distribution, a parameter θ is introduced to the probability model as a continuous random variable. The distribution of θ, when symmetric, acts as guarantor that the resulting distribution of the N DS random variable is bell-shaped and defined on a finite interval. We provide the marginal density of this new distribution and derive its properties and characterization. The distribution’s symmetric shape along with its bounded support, make it an attractive alternative to the normal distribution when modelling real-life phenomena observed over a finite interval. The distribution’s suitability for such situations is demonstrated using both simulated and real data.