What is one of the implications of the central limit theorem for inferential statistics?

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The central limit theorem states that, given a sufficiently large sample size, the sampling distribution of the sample mean will approximate a normal distribution, regardless of the shape of the population distribution from which the samples are drawn. This is particularly important in inferential statistics because it allows statisticians to make inferences about population parameters using the normal distribution as a model for the sampling distribution.

As sample sizes increase, the means of these samples will cluster around the true population mean, and the distribution of these sample means will tend to form a normal distribution. This justifies the use of the normal distribution for large samples, enabling the application of various statistical methods that rely on the properties of normality, such as hypothesis testing and confidence intervals. Thus, answer B accurately reflects this key implication of the central limit theorem within the realm of inferential statistics.