> I’m curious why each X_i has to be a sample of size 50 and can we just have each person roll the dice 1 time? Smaller samples have higher variance and their

> I’m curious why each X_i has to be a sample of size 50 and can we just have each person roll the dice 1 time? Smaller samples have higher variance and their means probably won’t converge as fast to a normal distribution. “Samples” of one, in isolation, have no defined variance and you can’t use them to infer anything.