Assume X~$\displaystyle N(\mu,\sigma)$. If we take a random sample of size n, how do we calculate that the probability of the average of the sample is at least $\displaystyle \mu+c \quad \forall{C}\in{\mathbb{R}}$. ie

$\displaystyle P(X_1+X_2+\cdots+X_n \geq n\cdot (\mu+C))$