This study?s main goal is to define approximate statistical convergence in spaces with probabilistic norms. The idea of convergence in random 2-normed space is more generalized as a result of our demonstrations of some fundamental features and examples of convergence in linear spaces with norms. More specifically, we demonstrate the findings for sets of statistical limit points and sets of cluster points of approximate statistically convergent sequences in these spaces. Additionally, we extend the idea of rough convergence by applying the idea of ideals, which automatically expands the original ideas of rough statistical convergence and rough convergence. We define the collection of rough ideal limit points and demonstrate a number of outcomes related to this collection.