was Parrish a college graduate?

There was no mention of Parrish having a college degree in the movie. At the beginning, he was just leaving a job he had on a ferry boat.

As for his age, his mother said that Paige was three years younger than he was. She had two birthdays while he was away in the Navy, the last being her eighteenth. So at the beginning of the movie, she was sixteen, and he must have been nineteen.

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He was never an on-campus student. He was in the Navy and, to train for and serve on a nuclear submarine, he would have had to enlist for six years. He'd have had the time and opportunity to acquire a degree by extension and-or correspondence courses, which, I believe, were just coming into vogue around that era.