A local project being analyzed by PERT has 42 activities, 13 of which are on the critical path. If the estimated time along the critical path is 105 days with a project variance of 25, what is the probability that the project will be completed in 95 days or less?

the probability that the project will be completed in 95 days or less, P (x ≤ 95) = 0.023

Step-by-step explanation:

This is a normal probability distribution question.

We'll need to standardize the 95 days to solve this.

The standardized score is the value minus the mean then divided by the standard deviation.

z = (x - xbar) / σ

x = 95 days

xbar = mean = 105 days

σ = standard deviation = √ (variance) = √25 = 5

z = (95 - 105) / 5 = - 2

To determine the probability that the project will be completed in 95 days or less, P (x ≤ 95) = P (z ≤ (-2))

We'll use data from the normal probability table for these probabilities

P (x ≤ 95) = P (z ≤ (-2)) = 0.02275 = 0.023