Suppose $X_1, X_2, \dots, X_9$ are i.i.d. $N(\mu, 1)$ and $\bar{X} = \frac{1}{9}(X_1 + X_2 + \dots + X_9)$. \\
What is the joint probability, computed up to three places after decimal, that $\bar{X} - \mu$ is greater than $\frac{1}{3}$ and $\sum_{i=1}^{9} (X_i - \bar{X})^2$ is greater than 5?