Final answer:
The cranial nerve that does NOT transmit information associated with a special sense is the oculomotor nerve (A).
Step-by-step explanation:
The cranial nerve that does NOT transmit information associated with a special sense is the oculomotor nerve (A). The oculomotor nerve is responsible for eye movements and controlling the muscles that lift the upper eyelid and constrict the pupil, but it does not transmit sensory information related to a special sense like smell, vision, hearing, or taste.
The other cranial nerves mentioned in the options - optic nerve (B), olfactory nerve (C), and vestibulocochlear nerve (D) - are all involved in transmitting sensory information associated with special senses.