A construction company has taken up a project to build a high-rise office complex. The time required to complete a construction project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks. A construction company must pay a penalty if the project is not finished by the due date in the contract.

(a) If a construction company bidding on this con- tract puts in a due date of 80 weeks, what is the probability that they will have to pay a penalty?

(b) If a construction company bidding on this con- tract wishes to be 90% sure of finishing by the due date, what due date (project week #) should be negotiated?