Confidence interval for normal mean

Let $X_1, X_2, \dots, X_{16}$ be a random sample from a $N(4\mu, 1)$ distribution and $Y_1, Y_2, \dots, Y_8$ be a random sample from a $N(\mu, 1)$ distribution, where $\mu\in\mathbb{R}$ is unknown. Assume that the two random samples are independent. If you are looking for a confidence interval for $\mu$ based on the statistic $8\bar{X}+\bar{Y}$, where $\bar{X}=\frac{1}{16}\sum_{i=1}^{16}X_i$ and $\bar{Y}=\frac{1}{8}\sum_{i=1}^8 Y_i$, then which one of the following statements is true?