Question

Your company is considering submitting a bid on a major project. You determine that the expected completion time is 100 weeks and the standard deviation is 10 weeks. It is assumed that the normal distribution applies. You wish to set the due date for the project such that there is an 85 percent chance that the project will be finished by this time. What due date should be set

Answer 1

To have an 85 percent chance of completing a project by the due date, with a mean completion time of 100 weeks and standard deviation of 10 weeks, the due date should be set to 110.4 weeks. This is calculated using the Z-score for the 85th percentile, which is 1.04, applying the formula X = mean + (Z-score * standard deviation).

Step-by-step explanation:

To set a due date with an 85 percent chance that the project will be finished by this time, given a normal distribution with an expected completion time (mean) of 100 weeks and a standard deviation of 10 weeks, we need to use the concept of normal distribution and Z-scores.

First, we need to find the Z-score that corresponds to the 85th percentile. This is typically found using a Z-table or statistical software. The Z-score for the 85th percentile is approximately 1.04. Once we have the Z-score, we can use the formula:

X = μ + (Z * σ)

Where:

X = the due date

μ = the mean (expected completion time, which is 100 weeks)

Z = Z-score (which is 1.04 for the 85th percentile)

σ = the standard deviation (which is 10 weeks)

Now, substituting the values into the formula:

X = 100 + (1.04 * 10)

X = 100 + 10.4

X = 110.4 weeks

The due date should be set at 110.4 weeks to have an 85 percent chance of completing the project by this time.

Answer 2

Due date to be set is 110 weeks

Step-by-step explanation:

Expected completion time = 100 weeks

Standard deviation, s = 10 weeks

P(x<k) = 0.85

P(Z<(k-u)/s) = 0.85

from the standard normal distribution table 0.85 = P(Z<1.037)

(k-u)/s = 1.307

k = 110.37 weeks