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 teachers as an example. We employ a nonparametric density estimator that explicitly accounts for measurement error using data from the Tennessee STAR experiment, and longitudinal data from North Carolina and Washington. 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 8-17 student percentile ranks, as compared to a change of 2-7 student percentile ranks for a 10 percentile change in teacher productivity in the middle of the distribution.