Theoretically, it is the distribution of a statistic based on all possible samples of a given size. In practice, it may be the distribution under repeated samples.
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A random distribution is a random sample set displayed in the form of a bell curve. See random sample set.
A set of probabilities over the sampling distribution of the mean.
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.
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in order to calculate the mean of the sample's mean and also to calculate the standard deviation of the sample's