which of the following statements about the sampling distribution of the sample mean, x-bar, is true? check all that apply. the distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. the distribution is normal regardless of the sample size, as long as the population distribution is normal. the distribution's mean is the same as the population mean. the distribution's standard deviation is smaller than the population standard deviation.

The sampling distribution of the sample mean refers to the mean of the sample drawn from a particular population. The statements are all true.

The larger the sample size, the closer the sample is to normality irrespective of the shape of the population distribution.

The mean of the sample distribution is the same as the population mean while the standard deviation of the sampling distribution is smaller.

When the population distribution is normal, then, the distribution mean would also be normal irrespective of the sample size.

Hence, all the statements are true.

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