A clinic's long-term average appointment duration is $50$ minutes. After a scheduling change, a sample of $n=10$ appointment lengths (in units of minutes) is recorded: $45,51,47,49,50,52,46,48,53,44$. To perform a null bootstrap under $\mu =50$, what is the null-centered sample $\left\{x_i^{\left(0\right)}\right\}$?

$\{45.0,51.0,47.0,49.0,50.0,52.0,46.0,48.0,53.0,44.0\}$

$\{44.5,50.5,46.5,48.5,49.5,51.5,45.5,47.5,52.5,43.5\}$

$\{49.5,55.5,51.5,53.5,54.5,56.5,50.5,52.5,57.5,48.5\}$

$\{46.5,52.5,48.5,50.5,51.5,53.5,47.5,49.5,54.5,45.5\}$