The sample mean is not always equal to the population mean but if we take more and more number of samples from the population then the mean of the sample would become equal to the population mean.
The Central Limit Theorem states that we can have a normal distribution of sample means even if the original population doesn't follow normal distribution, But we have to take a lot of samples.
Suppose a population doesn't follow normal distribution and is very skewed then we can still have sampling distribution that is completely normal if we take a lot of samples.
