The correct statement which is incorrect from the options about the sampling distribution of the sample mean (a) the standard deviation of the samplin

Here, for option (a):
This option is correct because if a sample is larger, it provides more information about the population which allows us to predict more accurate values. This means that the variability decreases if the predictions are more accurate.
For option (b):
This option is correct because the standard deviation of a sampling distribution of a sample mean and the variability of the sample mean over all possible samples are same.
For option (c):
This option is correct because a population mean has an unbiased estimator which is the sample mean.
For option (d):
This option is correct because the variation is given by the standard deviation of the sampling distribution.
For option (e):
This option is incorrect because the distribution of all possible sample mean is the sampling distribution and it cannot be centered about the sample mean (since there are many sample means).
Hence, the correct answer is (e).