Suppose a random sample of $n=16$ measurements is selected from a population with mean $\mu$ and standard deviation $\sigma$. For each of the following values of $\mu$ and $\sigma$, give the values of $\mu_{\bar{x}}$ and $\sigma_{\bar{x}}$.
a. $\mu=12, \sigma=3$
b. $\mu=144, \sigma=16$
c. $\mu=24, \sigma=28$
d. $\mu=12, \sigma=96$