Three-point estimates, both versions
Two formulas share the name, and a stem usually says which one it wants.
- Triangular (simple average): E = (O + M + P) / 3.
- Beta, also called PERT: E = (O + 4M + P) / 6, which gives the most likely value four times the weight.
- Standard deviation for the beta version: (P − O) / 6.
Worked example: an activity is optimistic at 4 days, most likely at 7 and pessimistic at 16. Triangular gives (4 + 7 + 16) / 3 = 9 days. Beta gives (4 + 28 + 16) / 6 = 8 days, with a standard deviation of (16 − 4) / 6 = 2 days. The long pessimistic tail pulls the simple average further than it pulls the weighted one.
If the stem says PERT or beta, use the weighted formula. If it says triangular or simple average, use the plain one. If it names neither, compute both and compare them with the options.
Schedule terms
- Work breakdown structure
- A hierarchical breakdown of the total scope into deliverables. The 100% rule: the WBS contains all of the project’s work and nothing outside it, and each level adds up to its parent.
- WBS dictionary
- The description behind each WBS element: what it includes, who owns it, acceptance criteria.
- Control account
- A management point where scope, cost and schedule are integrated and compared with earned value.
- Dependency types
- Finish-to-start (the usual one), start-to-start, finish-to-finish and start-to-finish. Separately, a dependency can be mandatory, discretionary, external or internal.
- Lead and lag
- A lead lets a successor start early; a lag makes it wait. Starting the user manual two weeks before the final build is a lead. Waiting a week after invitations go out before ordering catering is a lag.
- Critical path
- The longest path through the network, which sets the shortest possible project duration. Activities on it normally have zero total float.
- Total float and free float
- Total float is how long an activity can slip without moving the project finish. Free float is how long it can slip without delaying its next activity.
- Crashing and fast tracking
- The two compression techniques. Crashing adds resources to shorten critical activities; fast tracking overlaps activities planned in sequence.
- Resource leveling and smoothing
- Both fix resource conflicts. Leveling may move the end date; smoothing works only within float.
A small network, drawn as bars
Schedule cards
Decomposition, dependencies, compression and resource conflicts, with a few calculations. Keep scratch paper nearby; the notes show the arithmetic.
Practice cards here are written for study, not taken from PMI. The real CAPM mixes multiple choice with drag-and-drop, hot spot, comic-strip and video items.
Card 01 of 22 · 0 done · 0 right
To do 22
Doing
Card 01 of 22
While decomposing the scope of a book-delivery project, the team reaches deliverables small enough to be estimated, scheduled and assigned to one owner. What are these lowest-level WBS components called?
Note on A
Correct: Work packages are the lowest level of the WBS, where work can be reliably estimated, scheduled, and assigned to one owner.
Note on B
Activities are the schedule steps that result from decomposing work packages; they are not WBS components.
Note on C
Control accounts are management points above work packages where scope, cost, and schedule are integrated.
Note on D
Planning packages hold known work content that has not yet been detailed into activities.
Card 02 of 22
After plastering is finished, the walls must dry for two days before painting can start. How should this two-day wait be shown in the schedule?
Note on A
A buffer is time added to protect a schedule or chain, not a required wait between two linked activities.
Note on B
Float is flexibility an activity has before delaying others; it is not a required wait between activities.
Note on C
A lead lets a successor start before the predecessor finishes, which is the opposite of a wait.
Note on D
Correct: A lag is a required delay between the end of one activity and the start of the next, such as drying time.
Card 03 of 22
On a predictive project, a critical path activity is delayed by 3 days, and an activity with 5 days of total float is delayed by 4 days. Assuming no other changes, what is the effect on the project end date?
Note on A
Correct: The critical activity’s 3-day delay moves the end date by 3 days, while the other activity’s 4-day delay is absorbed by its 5 days of float.
Note on B
The delays are not added together; the non-critical activity has enough float to absorb its delay.
Note on C
Any delay on the critical path delays the project end date unless it is recovered.
Note on D
The 4-day delay is within the activity’s 5 days of float, so it does not drive the end date.
Card 04 of 22
A project team begins defining activities before the WBS has been stabilized. Which risk is most likely to materialize?
Note on A
The WBS dictionary describes work packages and does not set a limit on the number of activities.
Note on B
Control accounts are placed above work packages; defining activities early does not change that.
Note on C
Calculating the critical path before baselining is normal and is not a risk.
Note on D
Correct: Without a stable WBS, activities are not tied to agreed scope, so some work may be missed and some duplicated.
Card 05 of 22
Under rolling wave planning, a WBS component below a control account has known work content but no detailed activities yet. What is this component called?
Note on A
Correct: A planning package sits below a control account with known work content but no detailed activities yet, which fits rolling wave planning.
Note on B
A control account is the management point above work packages and planning packages, not the component itself.
Note on C
A summary activity groups schedule activities; it is not a WBS component awaiting detail.
Note on D
A work package already has enough detail to be estimated and broken into activities.
Card 06 of 22
Each element of a project’s WBS is given a unique identifier such as 1.2.3. What is the main purpose of this numbering?
Note on A
Correct: The code of accounts gives each WBS element a unique identifier so costs can be summarized and each element tracked.
Note on B
WBS numbers reflect structure, not business priority.
Note on C
The WBS shows what is delivered, not the order in which work is done; sequence comes from the schedule.
Note on D
Durations are set in the schedule; the identifier only labels the element.
Card 07 of 22
A project manager is building a WBS for a highly controlled, predictive infrastructure project with a 14-month duration. The sponsor expects weekly progress reporting and reliable estimates, and the team is debating how far to decompose each deliverable before estimating effort and assigning owners. Which approach to sizing work packages best supports accurate estimating and control without creating excessive administrative overhead?
Note on A
Correct: Work packages sized at roughly one to four weeks of effort are small enough to estimate and track reliably without excessive reporting overhead.
Note on B
Daily tasks with named owners are activity-level detail and create heavy administration in a WBS.
Note on C
A fixed size for every package ignores differences in complexity and natural deliverable boundaries.
Note on D
Phase-level packages are too large for reliable estimates and weekly progress control.
Card 08 of 22
The resource plan provides two engineers, but the schedule needs four at the same time on parallel activities. Which technique adjusts the schedule so it fits the engineers available, even if the end date moves?
Note on A
Correct: Resource leveling adjusts start and finish dates to match available resources, even if the end date moves.
Note on B
Crashing adds resources to shorten duration, which would require more engineers, not fewer.
Note on C
Fast tracking runs more work in parallel, which would increase the demand for engineers.
Note on D
Resource smoothing only adjusts work within float and cannot move the end date, so it cannot resolve a shortage this size.
Card 09 of 22
A work package “Concrete foundation” needs scheduling. Which set of items are appropriate schedule activities?
Note on A
Foundation design, site layout and permit approval are outputs or approvals that come before this work package, not the actions that build the foundation.
Note on B
A checklist, a quality plan and a report are documents; schedule activities are actions with a duration, not paperwork.
Note on C
Concrete foundation and reinforcement are deliverables or WBS components, so this set repeats scope elements instead of listing actions.
Note on D
Correct: Schedule activities are the actions needed to produce a work package, and pour, cure and inspect are actions with durations that can be sequenced.
Card 10 of 22
A project manager proposes crashing a critical-path activity by adding a second shift and paying overtime in order to recover a three-day delay. Before approving the request, which condition would make the proposed crashing option infeasible regardless of the available funding?
Note on A
Crash cost per day is normally higher than normal cost; that is a cost decision, not a reason the option cannot be carried out.
Note on B
A missing histogram is a planning gap that can be fixed, not a constraint that rules out crashing.
Note on C
Correct: A contractual cap on overtime and shifts makes adding hours impossible, no matter how much money is available.
Note on D
Zero float is expected for a critical path activity and is exactly why crashing it would help.
Card 11 of 22
A draft schedule assumes one database specialist works full time on three parallel activities. What is the MOST likely result if the schedule is baselined as is?
Note on A
Overallocation affects the dates, not just cost; the work cannot be done as scheduled.
Note on B
Assigning one person to parallel work does not shorten the path; the person cannot do it all at once.
Note on C
Correct: One specialist cannot work full time on three activities at once, so the baselined dates would not be achievable.
Note on D
Management reserve covers unknown risks, not a known resource conflict in the plan.
Card 12 of 22
An approved change request adds a new deliverable to the project scope, but the deliverable and its supporting work are not represented anywhere in the current WBS. What must the project manager do to keep the WBS compliant with the 100% rule?
Note on A
The risk register records uncertainties, not approved scope, so the WBS would still be incomplete.
Note on B
Correct: The 100% rule requires the WBS to contain all of the scope, so the new deliverable needs its own work packages.
Note on C
Stretching existing work packages hides the new deliverable instead of representing it in the WBS.
Note on D
The change was approved into this project’s scope, so moving it to another project contradicts the decision.
Card 13 of 22
A project is three weeks behind schedule against a fixed completion date. The organization recently absorbed significant rework costs when design and construction were overlapped on a similar effort, and the sponsor has stated that reliability of delivery matters more than speed. The design package is only 60 percent complete and a contingency reserve is available. Which compression approach is most appropriate?
Note on A
Correct: Crashing adds resources to critical activities without overlapping design and construction, so it avoids the rework risk the sponsor wants to avoid.
Note on B
Removing scope requires stakeholder approval and is not a schedule compression technique.
Note on C
Combining both still includes fast tracking, which brings back the rework risk, and no technique can guarantee the date.
Note on D
Overlapping design and construction while design is only 60 percent complete repeats the costly rework of the similar effort.
Card 14 of 22
A project has a fixed, non-negotiable completion date. Two non-critical activities are overallocated on a shared resource, and both have total float available. Which technique resolves the overallocation without delaying the finish date?
Note on A
Correct: Resource smoothing shifts work within available float to remove overallocation without changing the finish date.
Note on B
Fast tracking overlaps activities, which increases the demand on a shared resource rather than relieving it.
Note on C
Resource leveling can move the finish date, which this project cannot allow.
Note on D
Crashing shortens activities by adding resources; it is not the tool for spreading out an overallocated resource.
Card 15 of 22
A project schedule has an activity with an Early Start (ES) of 8 and a duration of 6. The activity’s nearest successor has a Late Start (LS) of 21 due to a forced milestone. Assuming a standard finish-to-start relationship with no leads or lags, what are the Early Finish (EF), Late Finish (LF), and Total Float (TF) for this activity?
Note on A
Setting LF equal to EF assumes the activity is critical, but the successor’s late start of 21 allows a later finish.
Note on B
A late finish of 15 does not match the successor’s late start of 21, so this float is miscalculated.
Note on C
Correct: EF = 8 + 6 = 14, LF equals the successor’s late start of 21, and total float = 21 − 14 = 7.
Note on D
Float is found by subtracting EF from LF, giving +7; a negative value would mean the activity is already late.
Card 16 of 22
The project’s final deliverables have passed quality inspection. Before the project is closed, which process is used to obtain the customer’s formal acceptance?
Note on A
Correct: Validate Scope is where the customer formally accepts deliverables that have already passed quality inspection.
Note on B
Close Project or Phase finalizes the project after acceptance and does not obtain acceptance itself.
Note on C
Control Quality checks deliverables internally for correctness; it does not secure customer acceptance.
Note on D
Manage Quality focuses on processes and does not involve formal acceptance of deliverables.
Card 17 of 22
Activity M has an early start of 5, an early finish of 12, a late start of 8, and a late finish of 15. Its only successor has an early start of day 14. What does this information mean for the project manager?
Note on A
Total float is LS − ES = 8 − 5 = 3 days, not 5, so this overstates the slack.
Note on B
Three days is the total float, but slipping 3 days would push M past its successor’s early start of 14.
Note on C
Correct: Free float is the successor’s early start minus M’s EF, 14 − 12 = 2 days, so M can slip 2 days without delaying it.
Note on D
Float is LS − ES or LF − EF, which equals 3 here; a late finish above the early finish means there is float.
Card 18 of 22
A project has two parallel paths: Path 1 (Activities A-B-C) with a duration of 45 days, and Path 2 (Activities A-D-E) with a duration of 38 days. To meet a compressed deadline, the project manager authorizes $4,000 to crash Activity D by 3 days, and $6,000 to crash Activity B by 2 days. Assuming no other dependencies, calculate the wasted project funds resulting from erroneously crashing non-critical activities.
Note on A
Ten thousand dollars counts both crashes, but the $6,000 spent on Activity B is not wasted because B is on the 45-day critical path.
Note on B
The $6,000 crash of Activity B shortens the critical path and is a valid use of the funds.
Note on C
Correct: Activity D is on the 38-day path, which is not critical, so the $4,000 spent crashing it does not shorten the project.
Note on D
No combination of the two crash costs produces $2,000; the waste is the full cost of crashing D.
Card 19 of 22
Which document defines that the critical path method will be used, how progress will be updated, and the variance threshold that triggers corrective action on dates?
Note on A
The project schedule is the output of scheduling, not the document that sets the method and thresholds.
Note on B
The schedule baseline is the approved schedule for comparison, not the rules for maintaining it.
Note on C
The requirements management plan covers requirements, not scheduling methods or thresholds.
Note on D
Correct: The schedule management plan sets the scheduling method, how progress is updated, and the variance thresholds for corrective action.
Card 20 of 22
A project network contains a primary critical path (Path A) with a total duration of 45 days. A parallel near-critical path (Path B) has a planned duration of 40 days. Due to a severe weather event, all activities on Path B experience a collective delay equal to 20% of their original planned duration. Simultaneously, Path A is delayed by a flat 2.5 days. What is the new project duration, and which path represents the new critical path?
Note on A
Path B grows to 48 days, not 49.5; this miscalculates the 20 percent delay.
Note on B
Path A becomes 47.5 days, but Path B at 48 days is now longer and sets the project duration.
Note on C
Path A becomes 47.5, not 48.5 days, and it is no longer the longest path.
Note on D
Correct: Path B becomes 40 × 1.2 = 48 days and Path A becomes 47.5 days, so Path B is the new critical path at 48 days.
Card 21 of 22
The scheduling team has gathered compression data for one critical activity. Under normal conditions the activity takes 20 days and costs $50,000. If the activity is crashed, its duration falls to 12 days and its cost rises to $74,000. What is the crash cost per day for this activity?
Note on A
Correct: Crash cost per day = (74,000 - 50,000) / (20 - 12) = 24,000 / 8 = $3,000 per day.
Note on B
$3,700 per day does not follow from the figures; the added cost of $24,000 spread over the 8 days saved gives $3,000.
Note on C
$6,166.67 comes from dividing the full crashed cost of $74,000 by 12 days, but crash cost per day uses only the extra cost and the days removed.
Note on D
$24,000 is the total extra cost of crashing; it still has to be divided by the 8 days saved to get a daily rate.
Card 22 of 22
To recover two weeks on the schedule, the project manager authorizes starting construction before the design package is fully approved, overlapping activities that were originally planned to run in sequence. Which risk is most likely to increase as a direct result?
Note on A
Overlapping work does not make the resource histogram less accurate; it changes when work happens.
Note on B
Fast tracking affects the critical path; reduced float on other paths is not the direct risk of overlapping design and construction.
Note on C
Fast tracking does not inherently add supervision costs; adding resources is crashing.
Note on D
Correct: Starting construction before design is approved means later design changes can force rework of work already built.
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Odds and ends
Is PERT the same thing as a three-point estimate?
PERT is one form of it, the beta-weighted version (O + 4M + P) / 6. A three-point estimate can also be the simple triangular average.
Where does schedule variance belong?
Schedule variance, EV minus PV, is an earned value measure under Task 2.3. It is covered with the other indices on cost and schedule variance.
What does the 100% rule mean for the WBS?
Every level of the WBS accounts for all of the work of the level above, no more and no less. Work missing from the WBS is outside the project’s scope.
Which plans set up the schedule in the first place?
The plan-based groundwork, including integration and change control, is on predictive processes and plans.