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It gets closer to 0.
As the slope get closer to zero, the graph becomes close to horizontal.
As the slope gets bigger the graph becomes closer to vertical - from bottom left to top right.
The sample mean is distributed with the same mean as the popualtion mean. If the popolation variance is s2 then the sample mean has a variance is s2/n. As n increases, the distribution of the sample mean gets closer to a Gaussian - ie Normal - distribution. This is the basis of the Central Limit Theorem which is important for hypothesis testing.