Answer
According to the central limit theorem, for a large sample size, the sampling distribution of $\bar{x}\ $ is approximately normal, irrespective of the shape of the population distribution. The mean and standard deviation of the sampling distribution of $\bar{x}\ $ are, respectively, $\mu_{\bar{x}}$ = $\mu$ and $\sigma _\bar{x}\ $ = $ σ /\sqrt n $.
Work Step by Step
According to the central limit theorem, for a large sample size, the sampling distribution of $\bar{x}\ $ is approximately normal, irrespective of the shape of the population distribution. The mean and standard deviation of the sampling distribution of $\bar{x}\ $ are, respectively, $\mu_{\bar{x}}$ = $\mu$ and $\sigma _\bar{x}\ $ = $ σ /\sqrt n $.
