Several studies pointed out the relevance of extrinsic noise in molecular networks in shaping cell decision making and differentiation. Interestingly, bimodal distributions of gene expression levels, that may be a feature of phenotypic differentiation, are a common phenomenon in gene expression data. The modes of the distribution often correspond to different physiological states of the system. In this work we address the role of extrinsic noise in shaping bimodal gene distributions in the context of microRNA (miRNA)-mediated regulation, both with stochastic modelling and simulations. MiRNAs are small noncoding RNA molecules that downregulate the expression of their target mRNAs. The titrative nature of the interaction is sufficient to induce bimodal distributions of the targets. We study the fluctuating miRNA transcription case to probe the effects of extrinsic noise on the system. We show that (i) bimodal target distributions can be obtained exploiting a noisy environment even in case of small miRNA-target interaction strength, (ii) an increase in the extrinsic noise shifts the range of target transcription rates that allow bimodality towards higher values, (iii) the protein half-life may buffer bimodal mRNA preventing its distribution from becoming bimodal and that (iv) in a noisy environment different targets may cross-regulate each other's bimodal distribution when competing for a shared pool of miRNAs even if the miRNA regulation is small. ; Comment: 26 pages, 8 figures