四、(10%) Let $X1, X2, \dots, Xn$ be a random sample from $N(\mu, \sigma^2)$ with known mean $\mu$. Moreover, Let $\chi^2{\mathfrak{p}(n)}$ denote the $100p^n$ percentile of $\chi^2(n)$, the Chi-Square distribution with $n$ degrees of freedom, where $0 \le p \le 1$. Namely, $P(Y \le \chi^2_{\mathfrak{p}(n)}) = p$, where $Y \sim \chi^2(n)$. Describe how you would construct a $100(1-\alpha)\%$ confidence interval for the unknown variance $\sigma^2$, where $0 \le \alpha \le 1$.