The skew and shape of the Molecular Weight Distribution (MWD) of polymers have a significant impact on polymer physical properties. Standard summary metrics statistically derived from the MWD only provide an incomplete picture of the polymer MWD. Machine learning (ML) methods coupled with high-throughput experimentation (HTE) could potentially allow for the prediction of the entire polymer MWD without information loss. In our work, we present a computer controlled HTE platform that is able to run up to 8 unique variable conditions for the free radical polymerizations of styrene. The segmented-flow HTE system was equipped with an inline Raman spectrometer and offline size exclusion chromatography (SEC) to obtain time dependent conversion and MWD respectively. In a supervised learning exercise, the gradient-boosted decision trees ML algorithm was used to predict monomer conversion from reagent concentrations and reaction time with high accuracy, using data obtained from the Raman spectra. A second ML algorithm uses the random forest regressor to predict entire MWDs of the synthesized polymer. Each algorithm can navigate the complexity of multiple parallel reactions occurring in a polymerization. The algorithm accurately predicts monomer conversion in the first case despite variations in the polymerization kinetic parameters over time. In the second case, we predict the polymer MWD where fine details such as the shape and skew of the MWD are captured without information loss. SHAP values were calculated to examine the dependence of the ML model output on the experimental conditions. A transfer learning approach was also used to enhance the predictive power of a Deep Neural Network (DNN) model in predicting batch polymerization MWDs. Overall, we demonstrate that the combination of HTE and ML provide a high level of predictive accuracy in determining polymerization outcomes, providing polymer chemists with the ability to target the synthesis of polymers with desired properties via the predicted conversion and MWD.