4 day old daughter seems to have motor skills and older child?

Hi. my newborn daughter(my first child :D) seems to already have slightly well developed motor skills. For instance, we played Beethoven's Moonlight Sonata last night to try to get her to calm down. About halfway through the song, she began to slowly wave her little arms back and forth *seemingly* to the tone of the music. She also had her forefinger and thumb in a pincer grasp(the way prude people are portrayed while drinking a beverage from a teacup). also, on her second day of life, the nurse at the hospital said that she rolled halfway over from her stomach to her side in just a few seconds while she( the nurse) had her back turned. I'm not sure if some of these things are something to make note of, or if they are just commonalities with infants and newborns these days(because of all of the exposure to the stimuli surrounding them before they even leave the womb). Any input?