Answer:
Explanation:
True. This statement is known as the Central Limit Theorem, which states that if random samples of size n are drawn from a population with a mean µ and standard deviation σ, then as n gets larger, the distribution of sample means approaches a normal distribution with a mean of µ and a standard deviation of σ/√n, regardless of the shape of the population distribution.
This is because the sampling distribution of the mean is based on the law of large numbers, which says that as the sample size increases, the sample mean will get closer to the true population mean. The standard deviation of the sample mean decreases with increasing sample size, leading to a normal distribution in the limit. Therefore, if the original population is normal or nearly normal, the distribution of the sample means will also be normal for any size sample.