For a given PERT activity, the standard deviation of the time needed to complete an activity is 3. If the optimistic time and the most likely time required to complete this activity are 8 and 12 minutes respectively. Find out the expected time in order to complete this activity.a)19.32 minutesb)13.67 minutesc)18.27 minutesd)13.01 minutesCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
- Standard deviation (σ) = 3
- Optimistic time (to) = 8 minutes
- Most likely time (tm) = 12 minutes

To find:
Expected time to complete the activity

Solution:
The expected time (te) can be calculated using the formula:

te = (to + 4tm + tp) / 6

where,
to = Optimistic time
tm = Most likely time
tp = Pessimistic time

Calculating Pessimistic time:
The pessimistic time (tp) can be calculated using the formula:

tp = 2tm - to

tp = 2 * 12 - 8
tp = 24 - 8
tp = 16 minutes

Calculating Expected time:
te = (to + 4tm + tp) / 6

te = (8 + 4 * 12 + 16) / 6
te = (8 + 48 + 16) / 6
te = 72 / 6
te = 12 minutes

Therefore, the expected time to complete the activity is 12 minutes.

Answer:
The correct answer is option B) 12 minutes.

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