What is the probability of completing the National Holiday Toy project in 93 tim
ID: 355892 • Letter: W
Question
What is the probability of completing the National Holiday Toy project in 93 time units?
1. Given the project information below, what is the probability of completing the National Holiday Toy project in 93 time units?
Act. ID
Description
Predecessor
Optm. (a)
Most likely (m)
Pess. (b)
Act timete
Variance
[(b 2a)/6]2
Critical
1
Design package
None
6
12
24
2
Design product
1
16
19
28
3
Build package
1
4
7
10
4
Secure patent
2
24
27
36
5
Build product
2
17
29
47
6
Paint
3, 4, 5
4
7
10
7
Test market
6
13
16
19
Act. ID
Description
Predecessor
Optm. (a)
Most likely (m)
Pess. (b)
Act timete
Variance
[(b 2a)/6]2
Critical
1
Design package
None
6
12
24
2
Design product
1
16
19
28
3
Build package
1
4
7
10
4
Secure patent
2
24
27
36
5
Build product
2
17
29
47
6
Paint
3, 4, 5
4
7
10
7
Test market
6
13
16
19
Explanation / Answer
Please find below table which calculates expected durations and Variance of each activity :
Act ID
Optimistic
Most likely
Pessimistic
Expected duration
Variance
1
6
12
24
13.00
9
2
16
9
28
13.33
4
3
4
7
10
7.00
1
4
24
27
36
28.00
4
5
17
29
47
30.00
25
6
4
7
10
7.00
1
7
13
16
19
16.00
1
Following are to be noted :
Expected duration = ( Optimistic duration + 4 x Most likely duration + Pessimistic duration ) / 6
Variance = ( Pessimistic duration – Optimistic duration)^2/36
Also please find below the precedence diagram of activities :
1
2
3
4
5
6
7
The parallel paths and their cumulative expected durations as follows :
1-2-4-6-7 = 77.33
1-2-5-6-7 = 79.33
1-3-6-7 = 43
Since 1-2-5-6-7 has the longest duration , it forms the critical path .
Variance of the critical path = 40
Therefore , standard deviation of the critical path = Square root ( 40) = 6.324
Let corresponding Z value of the probability of completing the project within 93 time units = Z1
Therefore .
Expected duration of critical path + Z1 x Standard deviation of critical path = 93
Or, 79.33 + 6.324.Z1 = 93
Or, 6.324.Z1 = 13.67
Or, Z1 = 13.67/6.324
Or, Z1 = 2.16
Corresponding probability for Z1 = 2.16 as derived from standard normal distribution table will be 0.98461
PROBABILITY OF COMPLETING THE NATIONAL HOLIDAY TOY PROJECT IN 93 TIME UNITS IS 0.98461
Act ID
Optimistic
Most likely
Pessimistic
Expected duration
Variance
1
6
12
24
13.00
9
2
16
9
28
13.33
4
3
4
7
10
7.00
1
4
24
27
36
28.00
4
5
17
29
47
30.00
25
6
4
7
10
7.00
1
7
13
16
19
16.00
1
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