Confidence bound from a pivotal minimum

Let $X_1, X_2, \dots, X_{10}$ be a random sample from the following probability density function $f(x) = \begin{cases} 2(x - \mu) e^{-(x-\mu)^2}, & x > \mu \ 0, & \text{otherwise} \end{cases}$, where $\mu \in (-\infty, \infty)$ is an unknown parameter. It is given that the observed value of $\min\{X_1, X_2, \dots, X_{10}\}$ is 1. Using the pivot $\min\{X_1, X_2, \dots, X_{10}\} - \mu$, suppose a 95% confidence interval of $\mu$ is of the form $(c, 1)$, then $c$ equals ________ (rounded off to two decimal places).