The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks.The construction company must pay a penalty if the project is not finished by the due date in the contract.If a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date, what due date (project week #)should be negotiated?
A)81.28
B)92.8
C)81.82
D).81954

Question

Quizplus · Accepted Answer

To ensure a 90% chance of finishing on time, we need to find the z-score corresponding to the 90th percentile of a standard normal distribution, which is approximately 1.28. Using the formula for a value in a normal distribution, $X = \mu + Z\sigma$, where $\mu = 80$ weeks, $\sigma = 10$ weeks, and $Z = 1.28$, we calculate $X = 80 + 1.28(10) = 80 + 12.8 = 92.8$ weeks. This means the company should negotiate a due date of 92.8 weeks to be 90% sure of finishing on time.

The Time Required to Complete a Project Is Normally Distributed