1. 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 dues date of 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?
92.8
Use z-scores.
Formula:
z = (x - mean)/sd
You are looking to solve for x, so fill in the rest of the formula with what you know.
Find z using z-table (problem gives you percentage). Mean = 80 and standard deviation = 10.
I hope this will help get you started.
88.1594
the time requested to complete a project is normally distributed with a mean of 80 weeks and 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 if finishing by the due date, what due date (project week number) should be negotiated?
To find the project week number that the construction company should negotiate in order to be 90% sure of finishing by the due date, we need to determine the corresponding z-score and use it to find the corresponding value in the standard normal distribution.
Here's how you can calculate it step by step:
Step 1: Convert the desired confidence level to a z-score.
The confidence level of 90% corresponds to a z-score of 1.645. You can find this value using a standard normal distribution table or a calculator.
Step 2: Calculate the standard error of the mean.
Since the project completion time follows a normal distribution with a mean of 80 weeks and a standard deviation of 10 weeks, we can use the formula for the standard error of the mean (SEM):
SEM = standard deviation / √(sample size)
In this case, the sample size is 1, so the SEM = 10 / √1 = 10.
Step 3: Calculate the due date by multiplying the SEM by the z-score and adding it to the mean.
Due date = mean + (z-score * SEM)
Due date = 80 + (1.645 * 10)
Step 4: Calculate the final result.
Due date = 80 + 16.45
Due date ≈ 96.45
Therefore, the construction company should negotiate a due date of week 97 (rounded up from 96.45) in order to be 90% confident of finishing the project by the due date.