Final answer:
The statement is true; the Central Limit Theorem asserts that the distribution of sample means becomes approximately normal with a large sample size, commonly considered as more than 30 samples, regardless of the population's distribution.
Step-by-step explanation:
True, according to the Central Limit Theorem, the sampling distribution of means will approach a normal distribution as the sample size becomes larger, even if the population distribution is not normal. This is generally considered accurate when the sample size exceeds 30. The mean of the sampling distribution will be approximately equal to the mean of the population from which the samples are drawn. The standard deviation of this sampling distribution, known as the standard error, is the population standard deviation divided by the square root of the sample size.
The application of the Central Limit Theorem provides a fundamental basis in statistics for making inferences about population parameters based on sample statistics. By ensuring that the sample size is sufficiently large (often n > 30), statisticians can apply normal probability models to analyze sample means, despite the underlying population distribution. This theorem illustrates the law of large numbers, showing that as the sample size increases, the sample means tend to converge towards the population mean.