Question

There are four activities on the critical path, and they have standard deviations of 1, 2, 4, and 2. what is the probability that the project will be completed in 38 weeks if its expected completion time is 40 weeks?

Answer 1

The expected completion time is μ = 40 weeks.
The random variable, X = 38 weeks (the probable time)

If the standard deviation is σ, then the z-score is z = (x - μ)/σ.

Let us test the given standard deviations.
When σ=1,
z = (38-40)/1 = -2
From standard tables,
P(x<=38) = P(z<=-2) = 0.0228 =2.3%

When σ=2,
z = (38*40)/2 = -1
P(x<=38) = P(z<=-1) = 0.1587 = 15.9%

When σ=4,
z = (38-40)/4 = -0.5
P(x<=38) = P(z<=-0.5) = 0.3085 = 30.9%

Answers:
z=1 => 2.3%
z=2 => 16% (approx)
z=4 => 31% (approx)