1. The problem provides a hypothesis test with null hypothesis $H_0: X \geq 6.4$ and alternative hypothesis $H_a: X < 6.4$. 2. This is a left-tailed test since $H_a$ involves less than ($<$) 6.4. 3. In a normal distribution centered at 6.4, the critical region to support $H_a$ is the area to the left of some value less than 6.4. 4. Therefore, the graph that matches this test is a normal curve centered at 6.4 with the area to the left of a tick mark left of 6.4 shaded. 5. The other options shade areas to the right or both sides, which do not correspond to the left-tailed test defined here. Final answer: The correct graph shows a normal curve centered at 6.4 with the area left of a tick left of 6.4 shaded.