states that the sampling distribution of x is approximately normal when the sample is large.

This statement is referring to the Central Limit Theorem. The Central Limit Theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In other words, if the sample size is large enough, the sampling distribution of the mean will be approximately normal.