Yes, if that's your meaning of "normal", you should be able to avoid the extremes of
bipolar illness even in a worst case scenario. If you take control of your illness (by correcting a faulty diet, if there is one, maintaining good levels of high quality vitamin and mineral supplements, you may even be unaware that you have an illness.)

It takes your pro-active effort to help the illness go into remission.

We've questioned your meaning of "normal" because there really is no such thing. It's just a term used to describe a different form of behavior or feeling tone.

I would venture to say that a good psychiatrist can find something really wrong in almost everyone if he looks hard enough and closely enough. Did you know that only 7% of bipolar patients ever seek help for their illness? That leaves 93% of bipolar patients untreated for a lifetime. How unnecessary, when a teaspoon of medication can stabilize a chemical imbalance!

Take heart, you'll be better very soon.