Final answer:
Cranial nerve III, or the oculomotor nerve, comes out of the superior colliculus and is associated with the Edinger-Westphal nucleus. It innervates 4 muscles that control eye movements.
Step-by-step explanation:
The cranial nerve associated with the Edinger-Westphal nucleus and comes out of the superior colliculus is cranial nerve III, also known as the oculomotor nerve. The oculomotor nerve innervates 4 muscles: the superior rectus, inferior rectus, medial rectus, and inferior oblique. These muscles are responsible for various movements of the eyes.