Final answer:
The centrosome, which contains centrioles, is the organelle responsible for organizing chromosomes during cell division to ensure proper distribution to daughter cells.
Step-by-step explanation:
The organelle that plays a role in the distribution of chromosomes during cell division is the centrosome. Specifically, within the centrosome, you will find structures called centrioles, which are crucial in organizing the chromosomes before cell division to ensure that each daughter cell receives the correct number of chromosomes. The nucleus contains the genetic instructions for the production of proteins, but it does not organize chromosomes during cell division; that function is served by the centrosome. Ribosomes, which are found both in eukaryotic and prokaryotic cells, provide a framework for protein synthesis, and the rough endoplasmic reticulum is studded with ribosomes and plays a role in protein synthesis as well. Finally, mitochondria, which are responsible for energy production, do not have a direct role in chromosome organization during division.