4. Calculate the number average and weight average molecular weight and polydispersity index of a polystyrene sample that contains the following mole fraction distribution: (15 points) \begin{tabular}{|c|c|} \hline \( \mathbf{n} \) (mole fraction) & \begin{tabular}{c} Degree of \\ polymerization \end{tabular} \\ \hline 0.05 & 200 \\ \hline 0.10 & 500 \\ \hline 0.20 & 1500 \\ \hline 0.30 & 2500 \\ \hline 0.20 & 3000 \\ \hline 0.10 & 4000 \\ \hline 0.05 & 5000 \\ \hline \end{tabular}
