Question

The central limit theorem (CLT) predicts that sampling from a normally distributed population results in a normally distributed SDM. What would the shape of the SDM be if the population is Skewed? Why?

Answer 1

As per central limit theorem,

When the population is skewed, the shape of the sampling distribution of mean is normal (or bell) with large sample size (n>30)

since

The central limit theorem states that if you have a population with mean μ and standard deviation σ and large samples from the population with replacement, then the sampling distribution of means will be approximately normally distributed. This will hold true regardless of whether the original population is normal or skewed, provided the sample size is large (n > 30). If the population is normal, then the theorem satisfies even for samples smaller than 30. i.e. n < 30