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Time estimates of an activity in a PERT network are: Optimistic time to = 9 days; pessimistic time tp = 21 days and most likely time te = 15 days. The approximates probability of completion of this activity in 13 days is: Ops: A. 0.16 B. 0.34 C. 0.5 D. 0.84?
Most Upvoted Answer
Time estimates of an activity in a PERT network are: Optimistic time t...
Solution:
Given data:
Optimistic time to = 9 days;
Pessimistic time tp = 21 days;
Most likely time te = 15 days.
To find:
The approximate probability of completion of this activity in 13 days.
Formula used:
The formula used in PERT analysis for Expected Time (T) is as follows:
T = (to + 4tm + tp) / 6
Where,
to = Optimistic time
tm = Most likely time
tp = Pessimistic time
The formula used for standard deviation (SD) is as follows:
SD = (tp - to) / 6
The formula used for calculating z-score is as follows:
z = (x - T) / SD
Where,
x = Time taken to complete an activity
The formula used for probability calculation is as follows:
P(x <= t)="">
Where,
Φ(z) is the standard normal cumulative distribution function.
Steps to be followed:
Step 1: Calculate the Expected time (T)
T = (to + 4tm + tp) / 6
= (9 + 4(15) + 21) / 6
= 15 days
Step 2: Calculate the Standard deviation (SD)
SD = (tp - to) / 6
= (21 - 9) / 6
= 2 days
Step 3: Calculate the z-score for x = 13 days
z = (x - T) / SD
= (13 - 15) / 2
= -1
Step 4: Find the probability of completing the activity in 13 days
P(x <= t)="">
= Φ(-1)
= 0.1587
Therefore, the approximate probability of completion of this activity in 13 days is 0.1587 or 15.87%. Therefore, the correct option is A. 0.16.
Conclusion:
The approximate probability of completion of this activity in 13 days is 0.1587 or 15.87%.
Given data:
Optimistic time to = 9 days;
Pessimistic time tp = 21 days;
Most likely time te = 15 days.
To find:
The approximate probability of completion of this activity in 13 days.
Formula used:
The formula used in PERT analysis for Expected Time (T) is as follows:
T = (to + 4tm + tp) / 6
Where,
to = Optimistic time
tm = Most likely time
tp = Pessimistic time
The formula used for standard deviation (SD) is as follows:
SD = (tp - to) / 6
The formula used for calculating z-score is as follows:
z = (x - T) / SD
Where,
x = Time taken to complete an activity
The formula used for probability calculation is as follows:
P(x <= t)="">
Where,
Φ(z) is the standard normal cumulative distribution function.
Steps to be followed:
Step 1: Calculate the Expected time (T)
T = (to + 4tm + tp) / 6
= (9 + 4(15) + 21) / 6
= 15 days
Step 2: Calculate the Standard deviation (SD)
SD = (tp - to) / 6
= (21 - 9) / 6
= 2 days
Step 3: Calculate the z-score for x = 13 days
z = (x - T) / SD
= (13 - 15) / 2
= -1
Step 4: Find the probability of completing the activity in 13 days
P(x <= t)="">
= Φ(-1)
= 0.1587
Therefore, the approximate probability of completion of this activity in 13 days is 0.1587 or 15.87%. Therefore, the correct option is A. 0.16.
Conclusion:
The approximate probability of completion of this activity in 13 days is 0.1587 or 15.87%.
Community Answer
Time estimates of an activity in a PERT network are: Optimistic time t...
PERT Network Probability Calculation
Given data:
Optimistic time to = 9 days
Pessimistic time tp = 21 days
Most likely time te = 15 days
Finding Expected Time
The expected time (tE) can be calculated as follows:
tE = (to + 4tm + tp) / 6
where,
to = optimistic time
tp = pessimistic time
tm = most likely time
Substituting the given values in the above formula, we get:
tE = (9 + 4*15 + 21) / 6 = 15 days
Finding Variance
The variance (σ2) can be calculated as follows:
σ2 = [(tp - to) / 6]2
where,
to = optimistic time
tp = pessimistic time
Substituting the given values in the above formula, we get:
σ2 = [(21 - 9) / 6]2 = 2.67 days2
Finding Standard Deviation
The standard deviation (σ) can be calculated as follows:
σ = √σ2
Substituting the value of σ2 we get:
σ = √2.67 = 1.63 days
Calculating Probability of Completion in 13 Days
To calculate the probability of completion of the activity in 13 days, we need to use the normal distribution formula:
Z = (X - tE) / σ
where,
X = completion time
tE = expected time
σ = standard deviation
Substituting the given values in the above formula, we get:
Z = (13 - 15) / 1.63 = -1.23
Using the Z-table, we can find the probability corresponding to the Z-value of -1.23. The probability is 0.1093.
However, since we are interested in the probability of completion in 13 days OR LESS, we need to find the area under the normal distribution curve to the left of the Z-value of -1.23. This can be done by subtracting the probability from 0.5 (since the total area under the curve is 1):
P(X ≤ 13) = 0.5 + 0.1093 = 0.6093
Therefore, the approximate probability of completion of this activity in 13 days is 0.6093 or 60.93%. Option C is the correct answer.
Given data:
Optimistic time to = 9 days
Pessimistic time tp = 21 days
Most likely time te = 15 days
Finding Expected Time
The expected time (tE) can be calculated as follows:
tE = (to + 4tm + tp) / 6
where,
to = optimistic time
tp = pessimistic time
tm = most likely time
Substituting the given values in the above formula, we get:
tE = (9 + 4*15 + 21) / 6 = 15 days
Finding Variance
The variance (σ2) can be calculated as follows:
σ2 = [(tp - to) / 6]2
where,
to = optimistic time
tp = pessimistic time
Substituting the given values in the above formula, we get:
σ2 = [(21 - 9) / 6]2 = 2.67 days2
Finding Standard Deviation
The standard deviation (σ) can be calculated as follows:
σ = √σ2
Substituting the value of σ2 we get:
σ = √2.67 = 1.63 days
Calculating Probability of Completion in 13 Days
To calculate the probability of completion of the activity in 13 days, we need to use the normal distribution formula:
Z = (X - tE) / σ
where,
X = completion time
tE = expected time
σ = standard deviation
Substituting the given values in the above formula, we get:
Z = (13 - 15) / 1.63 = -1.23
Using the Z-table, we can find the probability corresponding to the Z-value of -1.23. The probability is 0.1093.
However, since we are interested in the probability of completion in 13 days OR LESS, we need to find the area under the normal distribution curve to the left of the Z-value of -1.23. This can be done by subtracting the probability from 0.5 (since the total area under the curve is 1):
P(X ≤ 13) = 0.5 + 0.1093 = 0.6093
Therefore, the approximate probability of completion of this activity in 13 days is 0.6093 or 60.93%. Option C is the correct answer.
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Time estimates of an activity in a PERT network are: Optimistic time to = 9 days; pessimistic time tp = 21 days and most likely time te = 15 days. The approximates probability of completion of this activity in 13 days is: Ops: A. 0.16 B. 0.34 C. 0.5 D. 0.84?
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Time estimates of an activity in a PERT network are: Optimistic time to = 9 days; pessimistic time tp = 21 days and most likely time te = 15 days. The approximates probability of completion of this activity in 13 days is: Ops: A. 0.16 B. 0.34 C. 0.5 D. 0.84? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Time estimates of an activity in a PERT network are: Optimistic time to = 9 days; pessimistic time tp = 21 days and most likely time te = 15 days. The approximates probability of completion of this activity in 13 days is: Ops: A. 0.16 B. 0.34 C. 0.5 D. 0.84? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Time estimates of an activity in a PERT network are: Optimistic time to = 9 days; pessimistic time tp = 21 days and most likely time te = 15 days. The approximates probability of completion of this activity in 13 days is: Ops: A. 0.16 B. 0.34 C. 0.5 D. 0.84?.
Time estimates of an activity in a PERT network are: Optimistic time to = 9 days; pessimistic time tp = 21 days and most likely time te = 15 days. The approximates probability of completion of this activity in 13 days is: Ops: A. 0.16 B. 0.34 C. 0.5 D. 0.84? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Time estimates of an activity in a PERT network are: Optimistic time to = 9 days; pessimistic time tp = 21 days and most likely time te = 15 days. The approximates probability of completion of this activity in 13 days is: Ops: A. 0.16 B. 0.34 C. 0.5 D. 0.84? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Time estimates of an activity in a PERT network are: Optimistic time to = 9 days; pessimistic time tp = 21 days and most likely time te = 15 days. The approximates probability of completion of this activity in 13 days is: Ops: A. 0.16 B. 0.34 C. 0.5 D. 0.84?.
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