Many statistical analyses were implicitly based on the normal distribution, and as a consequence, researchers would need to adopt the central limit theorem to perform the subsequent data analysis. When applying the central limit theorem, the sample size should be 30 or above in order to have the sampling distribution of sample means to be approximated to the normal distribution. Chang et al. (2006 and 2008) showed that when applying the central limit theorem, the sample size should vary depending on the probability distribution type. As a result, the present study examined if the sample size suggested by many textbooks for using the central limit theorem is appropriate. This study uses computer simulation on approximation of the binomial distribution to the normal distribution. It is to explore the minimum sample size required for a binomial distribution to approximate the normal distribution and be replaced by the normal distribution.