What is the approximate shape of the distribution of the sample means?

The approximate shape of the distribution of sample means is typically normal due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the shape of the population distribution. This normality holds true especially when the sample size is sufficiently large (usually n ≥ 30). The mean of this distribution will be equal to the population mean, and its standard deviation will be the population standard deviation divided by the square root of the sample size, known as the standard error.