a$.)$ Your company is considering submitting a bid on a major project. You determine that the expected completion time for the project is $100$ days, and that the standard deviation of the expected completion time is $8$ days. $($It is assumed that the normal distribution applies here.$)$ You wish to set the project completion date in your bid such that there is an $80\%$ chance that you will be able to complete the project by the date you have set. What due date should you set? $($Note: fractional dates are allowed.$)$

b$.)$ What is the probability that the project described above is done within $90$ days?