Question

Suppose that the following estimates of activity times (in weeks) were provided for the network shown below:

Activity	Optimistic	Most Probable	Pessimistic
A	4	6	8
B	2.5	4.5	5.5
C	5	6.5	8
D	4	5.5	8
E	6.5	7.5	9
F	2	3.5	5
G	7	9	12
H	5	6	13

What is the probability that the project will be completed. If required, round your answers to four decimal places.

1. Within 20 weeks?
2. Within 22.5 weeks?
3. Within 25 weeks?

Answer 1

Since Immediate Predecessors are not mentioned, I have assumed that other activity will get start once earlier one will be finished i.e; as per below path -

A-B-C-D-E-F-G-H

Below is the screenshot of the formula -

ESSE 2020 - Excel File Home Insert Page Layout Formulas Data Review View Help Tell me what you want to do * Define Name Fi Use in Formula Insert AutoSum Recently Financial Logical Text Date & Lookup & Math & More Name Function - Used - - Time Reference Trigº Functions Manager Create from Selection Function Library Defined Names fx ? A .l le - - Trace Precedents 5 Show Forr Trace Dependents Error Chec Remove Arrows - A Evaluate F Formula Auditing A14 P(X<20) Activity Optimistic Most Likely cocoa D E F G H I J Pessimistic Expected Time Variance ES EF LSLF =(B2+4*C2+D2)/6 =((D2-B2)/6)^2 0 =G2+E2 = J2-E2 =13 =(B3+4*C3+D3)/6 =((D3-B3)/6)^2 =H2 =G3+E3 = 3-E3 =14 =(B4+4*C4+D4)/6 =((D4-B4)/6)^2 =H3 =G4+E4 =J4-E4 =15 =(B5+4*C5+D5)/6 =((D5-B5)/6)^2 =H4 =G5+E5 =J5-E5 =16 =(B6+4*C6+D6)/6 =((D6-B6)/6)^2 =H5 =G6+E6 =J6-E6 =17 =(B7+4*C7+D7)/6 =((D7-B7)/6)^2 =H6 =G7+E7 =J7-E7 =18 I=(B8+4*C8+D8)/6 =((D8-B8)/6)^2 =H7 |=G8+E8 |=J8-E8 |=19 13 =(B9+4*C9+D9)/6 =((D9-B9)/6)^2 =H8 -G9+E9 5J9-E9 =H9| 112 11 Expected Duration =H9 Variance =SUM(F2:F9) SD =B12^(1/2) P(X<20) =NORM.DIST(20,B11, B13,1) P(X<22.5) =NORM.DIST(22.5, B11, B13,1) P(X<25) =NORM.DIST(25,B11, B13,1)

Below is the screenshot of the result -

S 2020 - Excel File Home Insert Page Layout Formulas Data Review View Help Tell me what you want to do Cut my Scientific Be Copy Paste Calibri V11 VA A BIU - - A Font S === = aby Wrap Text Merge & Center - $ - % Format Painter Clipboard Alignment Number B14 X Fax =NORM.DIST(20,111,113,1) J Activity B C D E F Optimistic Most Likely Pessimistic Expected Time Variance 6.00 0.44 4.5 4.83 1.00 6.50 0.25 0.44 0.17 3.50 0.25 0.69 7.00 1.78 G ES 0 6.00 10.83 17.33 23.00 30.58 34.08 43.25 OUWLUI H EF 6.00 10.83 17.33 23.00 30.58 34.08 43.25 50.25 I LS 0.00 6.00 10.83 17.33 23.00 30.58 34.08 43.25 6.00 10.83 17.33 23.00 5.67 7.58 30.58 NIMI OD 9.17 34.08 43.25 50.25 50.25 13 14 Expected Duration Variance SD P(X<20) P(X<22.5) P(X<25) 5.03 2.24381867 1.00515E-41 1.96379E-35 1.11749E-29