Problem $2.$ The following information has been computed for a project: Expected total time is $180$ days with a standard deviation of $12$ days. $(6$ pts$)$

Show your work. Round to $4$ decimal places. Circle$/$highlight your answers. You may use Excel to do the calculations, but do NOT submit any Excel files or screenshots! Write or type up your work and final answers below. $(6$pts$)$

a$.$ What is the probability that the project will be completed $15$ days before its expected completion date of $180$ days? $(3$pts$).$

b$.$ If you would like to be $90\%$ certain that the project will be finished before the due date, what due date $($project duration in days$)$ would you ask for? $(3$pts$).$