If the population distribution is symmetric,the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 15 observations.

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This is a valid rule of thumb commonly used in statistics courses as well as in practice. It is based on the central limit theorem, which states that under certain conditions, the sampling distribution of the mean tends to be normal regardless of the population distribution shape. The minimum sample size of 15 is used as a guideline to ensure that the distribution is close enough to normal to yield accurate results. However, it is important to keep in mind that this is only an approximation and may not always hold true, especially for small or highly skewed populations.

If the Population Distribution Is Symmetric,the Sampling Distribution of the Mean