Confidence interval based on the sample minimum

Let $X_1,X_2,X_3$ be a random sample from a continuous distribution with the probability density function

$$f(x)=\begin{cases}e^{-(x-\mu)}, & x>\mu,\ 0, & \text{otherwise.}\end{cases}$$

Let $X_{(1)}=\min\{X_1,X_2,X_3\}$ and $c>0$ be a real number. Then $\left(X_{(1)}-c,X_{(1)}\right)$ is a $97\%$ confidence interval for $\mu$, if $c$ (round off to 2-decimal places) equals __________