Is this normal I am 5' 2 and a half and 120 pounds?

Of course! The question is really: "am I comfortable with being 5'2 and a half and weighing 120 lbs." If you feel that you are too heavy, then diet and take off a few pounds; exercise and build up your muscles and abs.

The main thing is that there is a wide range of "normal" body sizes and weights for humans.