When the distribution of the original variable departs from normality, a sample size of 30 or more is generally considered sufficient for the normal distribution to approximate the distribution of the sample means. This rule is based on the Central Limit Theorem (CLT), which states that regardless of the shape of the population distribution, the sampling distribution of the sample mean will tend to be normal or nearly normal if the sample size is large enough, typically $n \geq 30$.

However, if the original distribution is highly skewed or has heavy tails, a larger sample size may be necessary to ensure a good approximation.

Would you like further explanation on the Central Limit Theorem or sample size considerations?

Here are 5 related questions you might find interesting:

1. How does the Central Limit Theorem apply to non-normal populations?
2. What happens to the distribution of sample means if the sample size is smaller than 30?
3. What is the effect of a sample size greater than 30 on the approximation?
4. How can you assess if a sample size is large enough for the CLT to apply?
5. How does skewness and kurtosis affect the sample size needed for normal approximation?

Tip: When dealing with small sample sizes from a non-normal population, consider using non-parametric methods instead of relying on the normal distribution approximation.