Intelligent reflecting surface (IRS) has recently been identified as a prominent technology with the ability of enhancing wireless communication by dynamically manipulating the propagation environment. This letter investigates a multiple-input single-output (MISO) system deploying distributed IRSs. For practical considerations, we propose an efficient design of passive reflecting beamforming for the IRSs to exploit statistical channel state information (CSI) and analyze the achievable rate of the network taking into account the impact of CSI estimation error. The ergodic achievable rate is derived in a closed form, which provides insightful system design guidelines. Numerical results confirm the accuracy of the derived results and unveil the performance superiority of the proposed distributed IRS deployment over the conventional centralized deployment.