Individual cells in clonal populations often respond differently to environmental changes; for binary phenotypes, such as cell death, this can be measured as a fractional response. These types of responses have been attributed to cell-intrinsic stochastic processes and variable abundances of biochemical constituents, such as proteins, but the influence of organelles is still under investigation. We use the response to TNF-related apoptosis inducing ligand (TRAIL) and a new statistical framework for determining parameter influence on cell-to-cell variability through the inference of variance explained, DEPICTIVE, to demonstrate that variable mitochondria abundance correlates with cell survival and determines the fractional cell death response. By quantitative data analysis and modeling we attribute this effect to variable effective concentrations at the mitochondria surface of the pro-apoptotic proteins Bax/Bak. Further, our study suggests that inhibitors of anti-apoptotic Bcl-2 family proteins, used in cancer treatment, may increase the diversity of cellular responses, enhancing resistance to treatment.