The sampling distribution of the sample mean often has approximately a normal distribution. As the sample size increases, the sampling distribution of the sample mean has a more bell-shaped appearance. For relatively large sample sizes, the sampling distribution is bell shaped even if the population is highly discrete or highly skewed. This is known as the

For this case the best answer would be the "Central Limit theorem" or CLT since we are assuming that we have a large sample size (n>30) so then all the conditions are satisfied to assume a normal distribution for the sample mean

Explanation:

Previous concepts

The central limit theorem states that "if we 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".

From the central limit theorem we know that the distribution for the sample mean is given by:

Solution to the problem

For this case the best answer would be the "Central Limit theorem" or CLT since we are assuming that we have a large sample size (n>30) so then all the conditions are satisfied to assume a normal distribution for the sample mean

see earlier answer