If we have a distribution of x values that is more or less mound-shaped and somewhat symmetrical, what is the sample size n needed to claim that the distribution of sample means from random samples of that size is approximately normal?

n = 30

If the original distribution of x values is known to be normal, do we need to make any restriction about sample size in order to claim that the distribution of sample means taken from random samples of a given size is normal?

Yes

Thanks

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