1. ## X~N(mu,sigma) Probability Averages

Assume X~ $N(\mu,\sigma)$. 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 $\mu+c \quad \forall{C}\in{\mathbb{R}}$. ie
$P(X_1+X_2+\cdots+X_n \geq n\cdot (\mu+C))$

2. Originally Posted by Pur
Assume X~ $N(\mu,\sigma)$. 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 $\mu+c \quad \forall{C}\in{\mathbb{R}}$. ie
$P(X_1+X_2+\cdots+X_n \geq n\cdot (\mu+C))$
Use the sampling distribution of the mean (see Sampling distribution - Wikipedia, the free encyclopedia)

3. As directed by Pur, sampling distibution of normals is another normal with mean=mu and std=sigma/sqrt(n).

-O