The mathematical learning of the central limit theorem has been widely discussed in scientific writings by researchers through various versions of proofs. The discussion of the central limit theorem in case application has also been carried out with many different cases. However, students need to be given an overview of the truth of the central limit theorem through a general application. The truth and accuracy of the central limit theorem can be studied through a simulation study. Through simulation with R software, students can perform parameter variations such as variations in the population distribution, variations in the sample size used, as well as the number of repetitions or replications in studying the central limit theorem. The accuracy of the central limit theorem through simulation is determined by looking at the trend of the sampling distribution of the mean sample in the form of a histogram. The simulation results state that, in general, the larger the sample size used, the closer the sampling distribution to the mean sample is to the normal distribution. For samples taken from a population that has a distribution that is closer to symmetrical, then for a sample size that is not too large, the distribution of the mean sample is closer to a normal distribution. However, for samples originating from an asymmetric distribution, a larger sample size is required to obtain a sample mean that is close to the normal distribution
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