Confidence interval for a difference of means

Let $X_1,X_2,X_3$ be a random sample from $N(\mu_1,\sigma^2)$ distribution and $Y_1,Y_2,Y_3$ be a random sample from $N(\mu_2,\sigma^2)$ distribution. Also, assume that $(X_1,X_2,X_3)$ and $(Y_1,Y_2,Y_3)$ are independent. Let the observed values of $\sum_{i=1}^3\left[X_i-\frac13(X_1+X_2+X_3)\right]^2$ and $\sum_{i=1}^3\left[Y_i-\frac13(Y_1+Y_2+Y_3)\right]^2$ be $1$ and $5$, respectively. The length (round off to 2 decimal places) of the shortest $90\%$ confidence interval of $\mu_1-\mu_2$ equals __________