1. The problem states that $X$ is a normal random variable with mean $\mu = 50$ and standard deviation $\sigma = 3$. We are given a z-score $z = -1.2$ and asked to find the corresponding value of $x$. 2. Recall the formula for the z-score: $$z = \frac{x - \mu}{\sigma}$$ 3. We can rearrange this formula to solve for $x$: $$x = z \cdot \sigma + \mu$$ 4. Substitute the given values: $$x = (-1.2) \times 3 + 50$$ 5. Calculate the product: $$-1.2 \times 3 = -3.6$$ 6. Add to the mean: $$x = 50 - 3.6 = 46.4$$ 7. Therefore, the value of $x$ corresponding to the z-score $-1.2$ is $46.4$.