Question

$A,B,C,D$ and $E$ are the 5 activities along the unique critical path of a $AOA$ network of activities. Their characteristics are as under:

Activity	A	B	C	D	E
Expected~duration,~days	7	6	11	14	5
Standard deviation, days	2	2	3	4	1

What is the possible range of project duration (in days)?

• A. 24.6 to 61.4
• B. 31.2 to 54.8
• C. 28.1 to 57.9
• D. 25.55 to 60.5

Answer 1

The correct option is D 25.55 to 60.5

Project duration, $t_e=7+6+11+14+5$
$=43$ days
Variance $=2^2+2^2+3^2+4^2+1^2=34$
Standard deviation $\sigma =\sqrt{34}=5.8$
Range of project duration = (Minimum time, Maximum time)
$\text{Minimum time}=(T-3\sigma =25.6)\text{days}$
$\text{Maximum time}=T+3\sigma =60.4\text{days}$