The shape of the sampling distribution of sample means becomes more normal as:

The sampling distribution of sample means tends to approach a normal distribution as the sample size increases, regardless of the shape of the population distribution. This phenomenon is a result of the Central Limit Theorem, which states that as the sample size becomes larger, the distribution of the sample means will become approximately normal, provided the samples are independent and drawn from a population with a finite mean and variance.

When the sample size is small, the sampling distribution may be skewed or have a different shape, which is reflective of the underlying population distribution. However, as the sample size increases, the effects of individual variations in the population diminish, and the distribution of the sample means converges to a normal distribution. Therefore, increasing the sample size enhances the reliability and accuracy of statistical inference, allowing for better estimation of population parameters.

In summary, choosing to increase the sample size leads to a more normal shape of the sampling distribution of sample means, supporting the principles derived from the Central Limit Theorem.