First, the numbers in your arrays are all integers, so they clearly aren't normally distributed.
Ignoring that problem, what exactly are you trying to test? Do the eight entries in your array follow the same distribution, or do they each have individual distributions? Assuming the latter, read up about the Multivariate normal distribution and Hotelling's T-square distribution.
And when you talk about "doing the same thing for every single outcome in my population," are you implying that the population is finite?