Abstract
In this paper, we establish B.-Y. Chen's optimal inequalities for statistical submanifolds involving Casorati curvature and the normalized scalar curavture in a statistical manifold of quasi constant curvature. The equality cases of these inequalities are also considered. Further, we provide some applications of our results. Moreover, as a new example we construct minimal statistical surface (statistical submanifold) of a statistical manifold of quasi constant curvature.