Ya I would not say it is NORMAL as in a very high percentage of kids are that way in infancy - those to me are signs over an overtired child who has been allowed to hit/scream/tantrum to have their needs met ... Infants are cause and effect oriented if it works to get their need met they repeat it of it does NOT they try something else ... all adults need to be sending that poor thing the message GENTLE HANDS and so forth otherwise you are in for challenges as she gets older at brewing that "problem solving strategy" later
It shocks me how many times I see parents allowing their infant to hit slap kick at them and they do not DO anything other that give the kid what they wanted ... Seriously regardless of the age that is NOT appropriate behavior!!!!