In Psychology normal is considered 68% centered around the average (34% each side of the average)on a normal distribution curve, and abnormal is the remaining 32% (16% each way). However, Abnormal and normal are NOT synonimous with good or bad. For example someone who has an IQ higher than 110 would be abnormal by definition, the same way a psychopath would be considered abnormal. So abnormal could be anything from having a particularly large shoe size to being ridiculously short. In that sense, everyone is abnormal in one way or another.
One thing I believe is that normal or abnormal depends on perspective. If you are a devout conformist, anyone who is different will be considered abnormal but in reality, it is very hard to define. Certain people enjoy different types of foods, music or clothing and get coined as strange or abnormal while others like the same things everyone else tends to like and is seen as normal. Sometimes what is mistaken for different is having a well-rounded perspective on life and arts. There are also people with radically different moral or cultural values that are out of the average person's "norm". In my opinion, it is all in the eyes of the beholder.
I had a friend who once told me, "Your problem is that you still think there are normal people in the world." That was over 20 years ago yet I think that statement is more true than any of us will ever know. What is normal? Is it a generational thing? In the 1940's and 1950's it was the family in Leave it to Beaver, Father Knows Best, and Ozzie and Harriet. That would not hold true today. So what is normal today? South Street, Bevis and Butthead or The Big Bang Theory? I don't think that anyone knows. But I think the norm now is to not have a norm. Which of course would then be normal.
Normal is a broad word when you are describing an entire person. Everybody is abnormal in many ways. No two people are the same and that is how it should be. People are unique and they have unique interests and personalities. Everyone's face even looks different like a snowflake. Don't use the word normal to talk about people.
I think that this very odd question can be answered in a very specific way, and that is to simply look at the definition of abnormal. As defined, to be abnormal means that you are not normal. As such, we cannot say that being abnormal is being normal, it doesn't work that way.