QUESTION $4[25]$ The following data relates to a project that you are managing: Time in days Activity Predecessor Optimistic $($a$)$ Most likely $($m$)$ Pessimistic $($b$)$ A $-6815$ B A $151622$ C A $5812$ D A $101218$ E B $121723$ F C;D $141621$ G E $161819$ H E $51014$ I F;H $369$ J G;H $81317$ K I;J $711154\mathrm{.}1$ Using the PERT formula, calculate the time $($t$)$ and variance for all activities. $(5)4\mathrm{.}2$ Construct the network diagram $($AON$)$ and identify all paths and show the critical path. $(10)4\mathrm{.}3$ Calculate the probability of completing this project within $80$ days. $(5)$