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We need to find this statement is true or false. " When the sample size is large, the mean of $\stackrel{¯}{X}$ is approximately equal to the mean of $X$."

When the sample size is big, the central limit theorem holds true. The sample mean is almost equal to $\stackrel{¯}{X}$.

We need to find this statement is true or false. " When the sample size is large, $\stackrel{¯}{X}$is approximately normally distributed."

When the sample size is big, the central limit theorem holds true. Then $\stackrel{¯}{X}$has a roughly normal distribution.

We need to find the statement is true or false. " When the sample size is large, the standard deviation of $\stackrel{¯}{X}$is approximately the same as the standard deviation of $X$."

When the sample size is big, the central limit theorem holds true. The standard deviation of $\stackrel{¯}{X}$is hence roughly equal to the sample mean's standard deviation.