Before I will try to answer that question, let me first define the word 'normal'.
adjective - conforming to the standard or the common, usual, not abnormal, regular, natural
psychology - approximately average in any psychological trait, as intelligence, personality, or emotional adjusment.
If I hear some one say "I am just a normal guy" my first thought is "Oh dear, I am so sorry!" because 'normal' sounds sooo boring to me! I do not know about you though. Maybe you love 'normal' because it is predictable, no unexpected surprises or actions. You marry a normal person and know it will be like that for the next 60 odd years or so. You know what time the other person wakes up, goes to bed, the newspaper he or she reads, the things you talk about, the job, the holiday destination, the same camp site where other normal people stay each summer again, the same beach, towel and suntan lotion. Just to name a few but here of course, my assumption of 'normal' might be completely wrong.
Maybe you are brought up 'normal' and find happiness, shelter and comfort in 'normal'. And there is nothing wrong with that if it works for you.
But it does not work for me.
In many ways I am not brought up 'normal' which does not mean I was brought up 'abnormal'.
I come from a family not being afraid to look for and find unexpected things in life. But also things that happened to us without looking for it, were hugged to make the best of it.
No, my life has never been and still is not boring, thank goodness.
I am afraid I haven't inherited normal genes from both sides of the family. Changes of directions in life were often more common than uncommon (here is a contradiction! :-)
So... is a writer / author a normal human being?
To me, everybody who is creative is not (quote)conforming to the standard or the common, usual, not abnormal, regular, natural (unquote). If you have the gift to create something from nothing, whether others like it or not, there is a little door in your brain which opens to show you what you can do, create or achieve.
And if you are not afraid to open that door even wider, you can achieve or create more then you imagined at first. Said that, I understand that not everyone is gifted with doors or the same amount of doors. Who cares, you only need one to do something creative.
I also understand that the fear for failure is lurking around the corner and if you fail, what would others think of it. Can you cope with the feeling of failure, are you afraid that people point at you saying you are a looser. Afraid loosing friends.... Oh yes, I can think of many reasons why you prefer to keep the doors in your brains shut.
But does this not stop you from being creative? Exploring your gifts, even if you think you don't have one, is an adventure for life. And you know what is truly beautiful? Your gifts are not all visible at once. It is not so that at the age of let's say 20, all your gifts suddenly pop up. No, sometimes and more often than not, they are there when something happens in your life. What ever you think of life, one thing is certain, you can not predict it! Fortunately you can't, it would kill all your skills and gifts.
Writers are 'fairly normal' people like you and me. Most of them live in houses, have family and friends, appreciate good food but they have a skill of making stories from scratch. Short stories, novels, poems. They play with words, sentences, chapters. They create people who don't exist who do things that they have never done before because the are invented by the writer. Maybe that is not normal. But definitely not abnormal!
Writing does not always come natural. Of course you must have the drive to write. Not everyone is a writer (or sculptor, photographer, marathon runner, back packer, bungy jumper etc).
It does not matter what you write and it does not always have to be published! If writing is just a way to express your self without offering it to the world, that is fine too. That is not abnormal.
Have I answered the question if writers are normal people? Is it abnormal when I confess I don't know?
Wishing you a wonderful weekend!