Question

If x follows a distribution not known to be normal, then to assume that the distribution of the sample mean is normal, what must be true about the sample size n ?

Answer 1

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n >=30).

If x follows a distribution not known to be normal, then to assume that the distribution of the sample mean is normal,n > 30 must be true for sample size