The correct answer is C) Master. The responsibility of ensuring that all hands are familiar with their duties, as specified in the muster list, lies with the Master (Captain) of the vessel. The Master is the person in command of the ship and is ultimately responsible for the safety and operation of the vessel, including the crew's familiarity with their emergency duties. The other options are incorrect because the department heads, safety officer, and Chief Mate do not have the same level of overall responsibility for the vessel and crew as the Master. While they may have specific roles in ensuring crew readiness, the Master has the primary duty to oversee and verify that all crew members are properly trained and aware of their assigned responsibilities.