In this paper, we investigate the movable antennas (MAs)-enabled multiple-input-single-output (MISO) systems, where the base station (BS) equipped with multiple MAs serves multiple single-antenna user. The delay-sensitive scenario is considered, where users refrain from periodically sending training signals to the BS for channel estimations to avoid additional latency. As a result, the BS relies solely on the statistical channel state information (CSI) to transmit data with a fixed rate. Under this setup, we aim to maximize the outage-aware sum rate of all users, by jointly optimizing antenna positions and the transmit beamforming at the BS, while satisfying the given target outage probability requirement at each user. The problem is highly non-convex, primarily because the exact cumulative distribution function (CDF) of the received signal-to-interference-plus-noise ratio (SINR) of each user is difficult to derive. To simplify analysis and without comprising performance, we adopt the statistical CSI based zero-forcing beamforming design. We then introduce one important lemma to derive the tight mean and variance of the SINR. Leveraging these results, we further exploit the Laguerre series approximation to successfully derive the closedform and tight CDF of the SINR. Subsequently, the outageaware sum rate expression is presented but still includes complex structure with respect to antenna positions. Facing this challenge, the projected gradient ascent (PGA) method is developed to iteratively update antenna positions until convergence. Numerical results demonstrate the effectiveness of our proposed schemes compared to conventional fixed-position antenna (FPA) and other competitive benchmarks.