Probabilistic Linear Discriminant Analysis (PLDA) has become state-of-the-art method for modeling $i$-vector space in speaker recognition task. However the performance degradation is observed if enrollment data size differs from one speaker to another. This paper presents a solution to such problem by introducing new PLDA scoring normalization technique. Normalization parameters are derived in a blind way, so that, unlike traditional \textit{ZT-norm}, no extra development data is required. Moreover, proposed method has shown to be optimal in terms of detection cost function. The experiments conducted on NIST SRE 2014 database demonstrate an improved accuracy in a mixed enrollment number condition.