I always get a bit annoyed when people say things like so, saying things like this or that aren't "normal". Nothing's normal, and yet everything is normal. There is no standard for anything, and yet there is a standard for everything.
To simplify: Do what works best for you, and what makes you the happiest. Everyone is different.
If a long-distance seems "normal" or not to you, but it works, and you like it (or, well, you like the person, I assume you would want to live close together with your partner), then by all means, go for it. Don't let others determine what is best for you, what is "normal". If you let others decide for you, especially when it comes to things such as love and your study/work, you probably won't be as happy, or wonder how it could have been if you made your own choice.
I myself am in a happy long-distance relationship. We've been together quite some time, we visit one another on a regular basis, and it's going very well. In fact, even better than in the beginning.
What could be argued with long-distance relationships is that some people simply can't handle it. They want to be able to be close to their mate, their partner, preferably whenever they want to be.
But I (and my mate as well) take a look at it from this perspective: We need to better learn how to communicate, for communicating is key, is... essential to a good relationship. Moreso with a long-distance one. Seeing as you cannot hug, kiss, etc. with one another, one key aspect which remains is the communication part.
Make no mistake however: communication will always be one of the most, if not the most, important aspect to make any relationship successful.
I find that long-distance relationship in my case 'forces' me and my partner in a way to communicate more. We hope that by practising, so to say, our communication through tha internet (emails, Skype, (Skype/phone)calls, etc.) we will take these skills more into real-life situations. And it does for us.
We both are better able to communicate with each other when we like or don't like something, thus preventing sometimes pretty awkward situations x3
Don't let others decide what is normal or best for you. if you and your mate are happy, then that should be enough. In my opinion, if my friends told me to break up with a person I love, I would tell them it is not thier decision to make. if they make a problem out of it, sorry, but that friendship is not worth this. A real friend would let me discover for myself what works for me, and what doesn't, and won't forbid me to do one or another. They can advise, but they may not control.
In other words: You decide what you want and works for you.