Trying to imagine up some percentage about "dysfunctional" is not something I'd ever do. Someone once said that someone else said to her, "Every family is dysfunctional." My reply to that was, "No, every family is not. Every family has problems (at least if the family has been around long enough and isn't, say, a couple with one or two babies under two and few other close family members in the mix). HOW a family deals with those problems can make the difference between who/what is "dysfunctional" and who/what is not.
Maybe I'm naive or stupid, but I very much believe there's such a thing as a perfectly "normal" family - but since people are not perfect, and since families are made up of people, I doubt there is such a thing as a "perfect" family (and if there is it's rare; and, again, it's probably small enough and/or young enough that it hasn't yet run into some of the complications/complicated matters that a larger and/or more mature family has had time to run into.
I do think, however, that (as with any relationship) people who are part of the many/mixed relationships within a family need to set aside their own ego when doing that is important, be aware of what's healthy for the family as a whole (and if they don't know then get help in learning what is), recognize and respect that each member of the family is an individual, and recognize and respect the (sometimes) several different combinations of relationships within the family.
Having said that, I do think that maybe over the last couple/few decades far too many people have grown up without the benefit of having really some of the "finer points of socialization" (within the family, but in general) and/or without having someone provide them with the healthiest understanding/perspective of how their own family works/should work; and I think that could be because too many people get to eighteen (and head out on their own) without learning those things while they were still home and available for the kinds of discussions needed.
Then again, while 100% perfect is not going to happen, if a family is a high-enough percentage "close to perfect" its members can generally overcome a lot of differences and flaws and handle them in a healthy way.
But, yes. I do think there are plenty of "normal" families. Some may not face the challenges that others do and may not be as tested as others. Still, I think there's "normal facing challenges" and then there's "dysfunction" (not always the same thing).