To see if the data is normal or not I used the 68-95-99.7.
As you can see both X and Y have similar numbers on all three of these standard deviation groups. The big question is whether the data is normal or not and the answer is no, this data is not normal. For both X and Y the two and three standard deviations away from the mean are close to what the rules tell us it should be but looking at the one standard deviation away from the mean in both cases are far off from 68%. But now lets take a look at the histograms that were made for the height and arm span's data.
As you can see both of these graphs are skewed ending in a final answer that this data is not normal. I know this because of the data not being symmetric, and symmetric means normality.