Yes it's normal and nothing out of the ordinary for all children to try a temper tantrum once in awhile at various ages. But in my opinion, you shouldn't tolerate it. They will most likely out grow them eventually if you do nothing, but some don't. Nothing worse than a large child throwing a tantrum or an adult even.
I always told mine from the beginning that tantrums aren't allowed and I would not listen to it. I carry my little ones to their crib and tell them in strong, firm terms that I will come get them when they stop screaming. When they calm down, I go get them and kiss on them and tell them that's much better.
My second child was pretty stubborn and I would have to go back once or twice and remind her why she was in her crib....Very firmly I would tell her when she stops screaming she can come out.
I've only had one incident in public with my oldest. And though many would think I'm a mean mommy, I spanked her. I tried to reason with her, I spoke to her, I left the area to go home, and when I put her in the car she kept screaming and tried to buck out of the seat...well that was it. I took her out of the car, spanked her little bottom, and told her firmly she would sit in her seat. She immediately stopped screaming, let me put her in her seat, and then she pulled her blanket over her face and eventually went to sleep.
She never pitched a tantrum again. I only had to remind her what happened before when she pitched a tantrum and she would stop.
She's six now and since school started, she has tried on a few occasions to stomp her feet or sit on the floor and pout...I've talked to her about this and explained that it is the same as a tantrum and I won't tolerate it. She's had to spend the afternoon in her room twice since kindergarten started for big kid tantrums. Lately I only need to remind her it isn't acceptable and she will straighten up.
We always talk about what is upsetting her, but I don't relent when I've made a decision...she just has to accept my decision.
It works for the two girls...we shall see if it works with my son who is 10 months old. No tantrums yet.