Say I wanted to determine what the perfect weight for a basketball player of a certain height is (e.g. 6'3).

Say I had a big enough sample size for this (obviously I dont and thus couldn't pinpoint it to an exact height, but might have to run a regression using height as a factor or something similar).

Could I simply look at tons of players of that height and assume all other factors (such as speed, length of arms relative to body height, hand-eye-coordination, ...) are normally distributed and thus (if all variables were statistically independent from weight) I would be able to only look at players 6'3 and judge at what weight they play most efficiently (by using something like a basketball efficiency score)? and thus determine what weight is best for this player?

I know this wouldnt be possible practically as quickness for example isnt statistically independent from body weight, etc. but technically would it be possible that way - if all variables that have to be considered were stat. independent from weight and I had a sample size of bigger than 30?

I realized my thread digressed a bit from the original title..and I have 2 questions:

a) would such an approach be possible (if all the assumptions I mentioned above were true)

b) would looking at 31 players really be enough? (Im really wondering if the assumption that a variable is normally distributed if there are more than 30 cases is a bit "optimistic" and thus a bad proxy)

I guess there's a reason why 30 is said to be the critical value when it comes to assuming normal distribution. Could somebody please try to explain this to me? Thanks!