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We use the Atacama Large Millimeter/submillimeter Array (ALMA) in Cycle 1 todetermine spectroscopic redshifts of high-redshift dusty star-forming galaxies(DSFGs) selected by their 1.4mm continuum emission in the South Pole Telescope(SPT) survey. We present ALMA 3mm spectral scans between 84-114GHz for 15galaxies and targeted ALMA 1mm observations for an additional eight sources.Our observations yield 30 new line detections from CO, [CI] , [NII] , H_2O andNH_3. We further present APEX [CII] and CO mid-J observations for seven sourcesfor which only a single line was detected in spectral-scan data from ALMA Cycle0 or Cycle 1. We combine the new observations with previously published and newmm/submm line and photometric data of the SPT-selected DSFGs to study theirredshift distribution. The combined data yield 39 spectroscopic redshifts frommolecular lines, a success rate of >85%. Our sample represents the largest dataset of its kind today and has the highest spectroscopic completeness among allredshift surveys of high-z DSFGs. The median of the redshift distribution isz=3.9+/-0.4, and the highest-redshift source in our sample is at z=5.8. Wediscuss how the selection of our sources affects the redshift distribution,focusing on source brightness, selection wavelength, and strong gravitationallensing. We correct for the effect of gravitational lensing and find theredshift distribution for 1.4mm-selected sources with a median redshift ofz=3.1+/-0.3. Comparing to redshift distributions selected at shorterwavelengths from the literature, we show that selection wavelength affects theshape of the redshift distribution.

The redshift distribution of dusty star forming galaxies from the SPT survey