Question

The time required to complete a project is normally distributed with a mean of 78 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?

Answer 1

Here in this scenario it is given that the time required to complete a project is normally distributed with a mean of 78 weeks and a standard deviation of 10 weeks.

Now we want we find the time in weeks a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date.

That means we need to compute the,

P(X<a) = 0.90

Using the standard normal distribution method we calculated as below,

The probability is calculated the standard normal distribution z-table.

Now from the above result we can say that the probability that the company completed his work in 91 weeks is 0.90.

That means the company 90 percent sure that they completed the work in 91 weeks.

a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date is 91 weeks.due date is 91 weeks should be negotiated.