Figure 5.6: Figure 5.4 Sampling Distribution of Means for Repeated, Random Samples of Size N = 2 from Small Texas Town The central limit theorem states that the sampling distribution of the mean will be normally distributed, no matter what the shape of the parent population is, as long as the sample size is large. Large means N ≥ 30. Here, even though the N for each sample is small (N = 2), the sampling distribution is starting to assume the shape of a normal distribution.