No that is not normal, could be you have a faulty battery or a lemon phone. A couple things that you can do do troubleshoot...
- Try charging your phone and then as soon as you get the notification its fully charged, unplug it and use it as normal. See what happens here.
- Buy a replacement battery, make sure its an OEM official Samsung battery.
- Try a factory reset if nothing else works.
- If all else fails... go to store and get a replacement.
I have had issues with previous phones that the battery would drain excessivly fast from 100% to 90% but once it got to 89% it evened out and drained more normal. What is your total time one battery charge when this occurs? It is also possible that the battery calibration is messed up. Are you rooted with a custom ROM or running stock?