Operations help? (Stdev of a job, planning a process)

[MathIsHardBarbie]

Can you help me with a problem for my operations class?

I'm looking for the average and stdev of two designs for a job process.

Let's say the job process has 3 steps.
step 1 -- avg 1 stdev 2
step 2 -- avg 2 stdev 2
step 3 -- avg 3 stdev 1

If one person does this sequentially then the average duration is 6 and the stdev is sqrt(2^2+2^2+1^2) = 3

But if 2 people split up step 1, and one person does step 2 and the other step 3, the average is 3.5 because it's the longer duration when both are working simultaneously, right?
Part 1: 1/2 + 2 = 2.5
Part 2: 1/2 + 3 = 3.5

But what's the stdev of this job process design?
Part 1: sqrt [(2^2) + (2^2)] = 2.83
Part 2: sqrt [(2^2) + (1^2)] = 2.45

Is the stdev of this format 2.45 because it's the stdev of Part 2, or is it 2.83, because that's the longer one?

Also, the stdev of step 1 is 2; do I need to reduce it somehow because two people are now participating in it?

Thanks!