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What is the probability of completing the project
written 8.3 years ago by gravatar for teamques10 teamques10 ★ 68k modified 2.8 years ago by gravatar for sagarkolekar sagarkolekar ★ 11k

The Three time estimate for different activities of a project are given below:-

Activity $T_0$ $T_m$ $T_p$
1-2 2 5 8
2-3 4 9 20
2-4 4 7 16
2-5 8 11 20
3-6 3 7 17
4-6 7 10 13
4-5 0 0 0
5-7 3 5 13
6-7 2 3 10
7-8 2 4 6
Z -2 -1 0 1 2
P % -2.28 15.87 50 84.13 97.72

What is the probability of completing the project in 35 Days?
construction management
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written 8.3 years ago by gravatar for teamques10 teamques10 ★ 68k •   modified 8.3 years ago

Step 1 :-

For critical activity only

$\sigma = \frac{t_p - t_o}{6}$

Activity $T_0$ $T_m$ $T_p$ $t_e = \frac{t_0 + 4t_m + t_p}{6}$ $\sigma$ $\sigma^2$
1-2 2 5 8 5 1 1
2-3 4 9 20 6    
2-4 4 7 16 8 2 4
2-5 8 11 20 12    
3-6 3 7 17 8    
4-6 7 10 13 10 1 1
4-5 0 0 0 0    
5-7 3 5 13 6    
6-7 2 3 10 4 1.33 1.768
7-8 2 4 6 4 0.66 0.435
            $\sum \sigma^2 = 8.203$

Step 2:-

enter image description here

Project duration = 31 days

Critical path =1-2-4-6-7-8

Step 3:-

The probability of completing the project in 35 days is

z = $\frac{\text{scheduled time-project duration}}{\epsilon}$

S.T.= 35 Days

P.D.= 31 Days

$\epsilon = \sqrt{\sigma^2} = \sqrt{8.203} = 2.86$

z = $\frac{35 - 31}{2.86} = 1.398$

From table given in question, interpolation

enter image description here

$\boxed{\therefore P \% = 89.54 \%}$
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