  The properties of the noncentrosymmetric superconductor
($\alpha$-$\textit{Mn}$ structure) Nb$_{0.5}$Os$_{0.5}$ is investigated using
resistivity, magnetization, specific heat, and muon spin relaxation and
rotation ($\mu$SR) measurements. These measurements suggest that
Nb$_{0.5}$Os$_{0.5}$ is a weakly coupled ($\lambda_{e-ph}$ $\sim$ 0.53) type-II
superconductor ($\kappa_{GL}$ $\approx$ 61) having a bulk superconducting
transition temperature $T_c$ = 3.07 K. The specific heat data in the
superconductive regime fits well with the single-gap BCS model indicating
nodeless s-wave superconductivity in Nb$_{0.5}$Os$_{0.5}$. The $\mu$SR
measurements also confirm $\textit{s}$-wave superconductivity with the
preserved time-reversal symmetry.
