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 puts in a due date of 80 weeks, what is the probability that they will have to pay a penalty?
A)0
B)1.000
C)0.500
D)1/8

Question

Quizplus · Accepted Answer

If the due date is set at 80 weeks and the project takes longer, the company will have to pay a penalty. From the given information, we know that the mean completion time is 80 weeks and the standard deviation is 10 weeks. We can use these values to calculate the z-score for the due date of 80 weeks:

z = (80 - 80) / 10 = 0

Since we are looking for the probability of the project taking longer than 80 weeks (resulting in a penalty), we need to find the area to the right of the z-score of 0 on a standard normal distribution table. This area is 0.500 or 50%.

Therefore, the probability of the company having to pay a penalty is 0.500 or 50%.

The Time Required to Complete a Project Is Normally Distributed