Consider Sampling from a Population Whose Proportion of Successes Is $\hat{p}$

Essay

Consider sampling from a population whose proportion of successes is p = 0.5. Asthe sample size, n, increases, some characteristics of the sampling distribution ofchange. Which of the following characteristics will change as n increases, and whatis the nature of the change?
a) The mean of the sampling distribution of $\hat{p}$
b) The standard deviation of the sampling distribution of $\hat{p}$
c) The shape of the sampling distribution of $\hat{p}$