Find the expected duration of the project and its variance according to the PERT model. b$.$ Based on the PERT model, what is the probability that the project will be completed within $13$ weeks? What due date has a $90$ percent chance $($or greater$)$ of being met? d$.$ If the project manager uses the PERT model and wants to give a customer a due date that has at least a $60$ percent chance of occurring, what is the earliest date that the project manager can promise the customer that the project will be completed?