Question

A project's completion time is uncertain and follows a normal distribution. The project has an expected completion time of 36 weeks, and with a project variance 7 weeks. The project manager wishes to determine the probability of finishing the project before the given deadline: 26 weeks from today. What is the corresponding z-value in determining the probability? Numbers only. keep 3-decimal if not exact, either round up or down is ok

Answer 1

The z-value for the probability of completing the project before 26 weeks, with an expected completion time of 36 weeks and a variance of 7 weeks, is approximately -3.774.

Step-by-step explanation:

To calculate the z-value for the probability of completing the project before 26 weeks when the mean completion time is 36 weeks and the variance is 7 weeks, we first need to find the standard deviation. The variance is the square of the standard deviation, so the standard deviation (σ) is the square root of the variance, which is √7 ≈ 2.646 weeks.

The z-value is then calculated using the formula: z = (X - μ) / σ, where X is the time we are interested in (26 weeks), μ is the mean (36 weeks), and σ is the standard deviation. Plugging the numbers into the formula gives us: z = (26 - 36) / 2.646, which results in z ≈ -3.774.