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Unformatted text preview: Case: Time, Please February 27, 2009  We ﬁrst need to ﬁnd out, to complete one path with probability 95%, how many weeks
are needed. Let Ti , where i = A, B, C , represent the number of weeks needed for path i. Then,
As the z score for 95% is 1.645, we have 1.645 = TA − 10
4 or TA = 16.58. Similarly, we have
1.645 = TB − 14
TC − 13
and 1.645 =
2 Therefore, TB = 17.29 and TC = 16.29, and we can conclude that to complete the project with
probability 95%, Smitty needs at least 17.29 weeks.
 (Optional) In the ﬁrst step, we have derived a lower bound. However, we still don’t
know exactly how many weeks are needed to complete the project with probability 95%? Let’s
ﬁrst consider a simpler case. Let’s assume that paths A, B, and C are independent of each
other. Then the probability of completing the project is the multiplication of the probability
of completing path A by that of completing path B and by that of completing path C; that is,
if we let ti , where i = A, B, C , represent the time required to ﬁnish path i. Then,
P rob(tA ≤ T ) × P rob(tA ≤ T ) × P rob(tC ≤ T ) = 95%, (1) and T is the time required to complete the project with probability 95%.
To ﬁnd T , I have developed an Excel spreadsheet (Solution for Time Please). In the spreadsheet, I increase T from 17 to 19. As you can see from the spreadsheet, T is about 18 weeks. 1 ...
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This note was uploaded on 05/21/2011 for the course ISOM 111 taught by Professor Hu,inchi during the Spring '10 term at HKUST.
- Spring '10