We consider the recently introduced notion of I-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509-1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826-830) in probabilistic normed spaces and in the following (Sencimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce the notions like strong I-statistical cluster points and extremal limit points, and strong I-statistical continuity and strong I-statistical D-boundedness in probabilistic normed spaces and study some of their important properties.