Whether it's normal is almost beside the point for me. My 14-year-old does this incessantly, and it is occasionally really difficult for me to deal with. She usually doesn't do it very loudly, but something about the timbre of her voice makes it cut through -- it's impossible to ignore even when she's doing it quietly.
Occasionally, she does it loudly, and then I feel totally justified in telling her to stop. But it appears to be a compulsion for her because sometimes we'll be right next to each other (e.g. watching a movie), and she'll stop after I ask her to, but 20 seconds later, she starts again. When I call her out, she apologizes. She just doesn't seem to realize she's doing it.
I actually have songs going through my head almost constantly, so I'm not surprised that she does. The difference is that I was never compelled to sing them aloud -- I just "play" them in my head. The only thing close to a solution I have is to ask her to do the same (i.e., just imagine the melody in her head) when it starts to feel like water torture to me.