The Central Limit Theorem is important in statistics because for a large n, it says the population is approximately normal for any normal population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the distribution for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Step-by-step explanation:

In probability theory, the central limit theorem (CLT) states that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (a symmetrical bell shaped curve symmetrical about the mean) even if the original variables themselves are not normally distributed. The theorem is very important in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions, provided sample sizes are large.

Thus out of the given options correct answer is

for a large n, it says the sampling distribution of the sample mean is approximately normal,