It's been along time since my Grandmas sister visited , and I do hope more people answer your question with recent experience, but from what I have been told , these visas that are granted are usually for older people ,Parents and Grandparents you have a chance, but if you are planning to invite your 20 year old cousin chances are slim.
But there are other ways of coming to the U.S. for a visit , for instance some trips are sponsored by Church Groups , many young Cubans have visited the U.S. this way.
If you happen to travel to Cuba , I believe the invitation you speak about is easier and less costly, also there are angencies that will process the invitation for you like Antillas Express of Canada , heres a link for the PDF , all you have to do is fill out the form and send it , Good Luck
http://www.antillas-express.com/formulaires/CARTA-...