For independent uniform variables on , subtracting the sum’s mean and dividing by its standard deviation puts every sum on the same scale. As the count grows, the standardized distribution approaches a normal distribution.对相互独立的 均匀随机变量，将和减去均值、再除以标准差，就能放在同一尺度上比较。项数增加时，标准化后的分布趋近于正态分布。
Green shows the exact standardized density for one through eight summands, not a sampled histogram. The gold curve is the standard normal density.绿色展示一至八项求和后标准化的准确密度，而非抽样直方图。金色曲线是标准正态密度。