Population and sample size?

Question

Consider two population distributions labeled A and B. Distribution A is highly skewed and non-normal, while the distribution B is slightly skewed and near normal. In order for the sampling distributions of A and B to achieve the same degree of normality

Answer 1

The central limit theorem tells us that for any random variable X that if we take a large enough sample from the population, the mean of the sample will be approximately normal.  

In this case the number of samples needed for A to have a mean that is normally distributed would be considerably larger than the sample size need for B to have a normal mean.