The central limit theorem is important in statistics because

a) for a large n, it says the population is approximately normal.
b) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size
c) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population
d) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.