It is common to assume that worker productivity is normally distributed, but this assumption is rarely if ever tested. We estimate the distribution of worker productivity where individual productivity is measured with error, using the productivity of elementary school teachers as an example. Proposals to improve teacher productivity often focus on the extreme tails of the productivity distribution, so we pay particular attention to the shape of the tails of the distribution. We do this using a nonparametric density estimator that explicitly accounts for measurement error. We use data from the Tennessee STAR experiment, and longitudinal data from North Carolina and Washington. While the exact productivity distributions differ among the three, the results are qualitatively similar. Statistical tests show that the productivity distribution of teachers is not Gaussian, but the differences from the normal distribution tend to be small. Our findings confirm the existing empirical evidence that the differences in the effects of individual teachers on student achievement are large and the assumption that the differences in the upper and lower tails of the teacher performance distribution are far larger than in the middle of the distribution. Specifically, a 10 percentile point movement for teachers at the top (90th) or bottom (10th) deciles of the distribution is estimated to move student achievement by 8 to 17 student percentile ranks, as compared to a change of 2 to 7 student percentile ranks for a 10 percentile change in teacher productivity in the middle of the distribution.