Consider Sampling from a Normal Population with a Population Mean $\bar{x}$

Essay

Consider sampling from a normal population with a population mean µ and standarddeviation ?. As the sample size, n, increases, some characteristics of the sampling distribution of the sample mean, $\bar{x}$ , may change. Which of the following characteristics will change as n increases, and what is the nature of the change?
a) The mean of the sampling distribution of $\bar{x}$
b) The standard deviation of the sampling distribution of $\bar{x}$
c) The shape of the sampling distribution of $\bar{x}$