The sampling distribution of sample mean for a large population is approximately normal if the sample size isans.

The sampling distribution of the sample mean for a large population is approximately normal if the sample size is large enough, typically if it is greater than or equal to 30. This is according to the Central Limit Theorem, which 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 fact, for such populations, even single values are considered to be normally distributed.