Pippa makes a good point, it is more common than people realise.
How common, when the person involved is the only one who diagnoses it, is hard to say. For those who have been diagnosed however, the probability is 100%.
As Izumi rightly points out, it is better to act sooner rather than wait, in my case for another 40+ years, but then again in the 1960's in Australia, transition was virtually non-existent. ( The first SRS procedure wasn't performed here until 1972 as far as I know.)
As a parent, I would caution against blurting out , "Mum I want to be a girl" too. Far better to take the path of asking their help with finding a therapist regarding issues of gender and identity, especially if you think you may be suffering form depresion too.
If you can stress that it is more than the usual teenag angst, they hopefully will want to help you sort things out. If the therapist says you have GID it will carry more authority. If you father is like most men, once he recognises it as a problem , he will be oriented to finding a way to fix it. Your mother on the other hand will probably react more emotionally.
Hope things work out , Sandra.