2 year old tantrums

So this is embarrassing, but I'm a first time mom and haven't dealt with a lot of toddlers other than my own daughter. She doesn't have many "meltdowns" and usually when she does it's because we've told her she can't do or can't have something. I figured this was pretty typical. Usually they don't last long. She cries and whines, maybe she will fall down to the floor and cry. I don't give in often, I just try to get down to her level and explain why we made the decision we made and try to give her other options. Occasionally she attempts to hit/bite, but we always talk about how we are supposed to use kind/gentle hands and biting is for food. Anyway, daycare had a talk with me about her screaming and about her hitting and biting when she's mad. I thought it was typical of most 2 year olds, and at least at home she rarely does it. Can you please tell me your toddler tantrum stories? Or at least tell me if this is normal behavior?