Assume for the following project that the duration of each activity follows a beta probability distribution with parameters a, m and b. Determine the probability that the project will be finished in 21 weeks or less. What must the deadline be set to if we want to have a 99% chance of completing the project on time? (book chapter 6 in Essentials ofManagement Science)

\begin{tabular}{lcccc} \hline Activity & Immediate predecessors & a & m & b \\ \hline A & & 1 & 2 & 3 \\ B & B & 2 & 3 & 4 \\ C & A, C & 3 & 4 & 6 \\ D & B & 3 & 5 & 8 \\ E & C & 4 & 5 & 6 \\ F & D, F & 5 & 7 & 10 \\ G & E, G & 3 & 4 & 5 \\ H & 1 & 2 & 3 \\ \hline \end{tabular}