If only Norman had really called the cops at the end (spoiler)

...he could have given the same explanation to them that he did Claire that she had killed herself and he had hidden the body in the lake to avoid exposure. Same kind of thing worked for Ted Kennedy! Then he and Claire could have had a good life together. The dead girl was a tramp anyway, would have effed up his career completely by running to the Dean. Really not a sympathetic victim if you think about it.