OH sorry no one answered your post, I must have missed it, I don't have alot of experience with this I have been bitten but not enough to hurt like that, I don't think its abnormal I think it just depends on the bird and why its biting I found this article that might be useful for you.
http://pet-birds.pet-breeds.com/Biting_Cockatiels.html
http://pet-birds.pet-breeds.com/Biting_Cockatiels.html