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A common rule of thumb is that a sample size of 30 is sufficient to assure that the sum of random variables is normally distributed by the Central Limit Theorem (CLT). The sample size depends on the skew of the population. So the uniform distribution, which is neither normal nor skewed, requires a relative small sample size for the sum of the sample to be approximately normally distributed. This script estimates the sample size using two methods from a sample of data.
Simple open the data table and then open and run this script. Select the data column with the data sample and assign it to the Y role, then click OK. A Distribution platform opens with the results appended to the bottom of the window.
Sugden, R. A., et al. (2002) Cochran's Rule for Simple Random Sampling, J. of the Royal Statistical Society, Series B, Statistical Methodology. 62(4):787-793.