STAT 290 Final Review Questions PDF

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STAT 290 Final Review Questions 1. Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes, λ = 1/10. a. What is the probability that a customer will spend more than 15 minutes in the bank? b. What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes?

2. If 3 persons, on an average, come to ABC company for job interview, then find the probability that less than three people have come for interview on a given day.

3. The deals cracked by an agent per day is a random Poisson variable with mean 2. Given that each day is independent of other day, find the probability of getting 2 deals cracked on first day and 1 deal to be cracked the next day.

4. What’s the major difference between PERT and CPM?

5. A) What is the critical path? B) What is a slack? 6. What is the difference between optimistic, pessimistic and most likely time?

7. What is the expected activity time, under PERT method?

8. What is crashing, crash time and crash cost?

9. Consider the following project information. Activity

Activity Time (weeks)

Immediate Predecessor(s)

A

3

none

B

4

A

C

2

B

D

5

B

E

4

C

F

3

D

G

2

E, F

9-1. What is the completion time for the project? a) 18 b) 15 c) 32 d) 17 e) 5

9-2. What is the critical path? 10. Consider this information about an activity: ES=12, EF=18, LS=14, and LF=20. What is the amount of slack associated with this activity? a) 6 b) 0 c) 8 d) 4 e) 2

11. Given the portion of a network shown below, what is the earliest finish time for activity C, if the earliest start time of A is 12, and the earliest start time of B is 13; and the activity time of A, B, and C are 4, 2 and 7 respectively? a) 23 b) 25 c) 26 d) 22 e) 24

12. In making a backward pass through a network, activities B and C are immediate successors of activity A, which has an activity time of 6. The latest finish times for activities B and C are 40 and 30 respectively. The activity times for activities B and C are 8 and 3. What is the latest start time for activity A? a) 32 b) 28 c) cannot be determined d) 21 e) 27

13. True/False questions a) The ES of an activity that has only one predecessor is simply the EF of that predecessor. b) One phase of a large project is scheduling c) PERT, but not CPM, has the ability to consider the precedence relationships in a project. d) The shortest of all paths through the network is the critical path e) Slack is the amount of time an activity can be delayed without delaying the entire project. f) Every network has at least one critical path. g) The PERT pessimistic time estimate is an estimate of the minimum time an activity will require. h) The standard deviation of the project duration is the average of the standard deviation of all activities on the critical path. i) In PERT analysis, the identification of the critical path can be incorrect if a noncritical activity takes substantially more than its expected time. j) Shortening the project’s duration by deleting unnecessary activities is called project crashing. k) In project management, crashing an activity must consider the impact on all paths in the network. 14. Which of the following statements regarding critical paths is true? a. The shortest of all paths through the network is the critical path. b. Some activities on the critical path may have slack. c. Every network has exactly one critical path. d. On a specific project, there can be multiple critical paths, all with exactly the same duration. e. The duration of the critical path is the average duration of all paths in the project network.

15. Which of the following statements regarding CPM is true? a. The critical path is the shortest of all paths through the network. b. The critical path is that set of activities that has positive slack. c. Some networks have no critical path. d. All activities on the critical path have their LS equal their predecessor's EF. e. All of the above are false. 16. A simple CPM network has three activities, A, B, and C. A is an immediate predecessor of B and of C. B is an immediate predecessor of C. The activity durations are A=4, B=3, C=8. a. The critical path is A-B-C, duration 15. b. The critical path is A-C, duration 12. c. The critical path is A-B-C, duration 13.5 d. The critical path cannot be determined without knowing PERT expected activity times. e. The network has no critical path. 17. A simple CPM network has three activities, D, E, and F. D is an immediate predecessor of E and of F. E is an immediate predecessor of F. The activity durations are D=4, E=3, F=8. a. The critical path is D-E-F, duration 15. b. The critical path is D-F, duration 12. c. Slack at D is 3 units d. Slack at E is 3 units e. Both a and c are true 18. A simple CPM network has five activities, A, B, C, D, and E. A is an immediate predecessor of C and of D. B is also an immediate predecessor of C and of D. C and D are both immediate predecessors of E. a. There are two paths in this network. b. There are four paths in this network. c. There are five paths in this network. d. There are 25 paths through this network. e. None of these statements is true.

19. Activity D on a CPM network has predecessor B and C, and has successor F. D has duration 6. B's earliest finish is 18, while C's is 20. F's late start is 26. Which of the following is true? a. B is a critical activity. b. C is completed before B. c. D has no slack but is not critical.

d. D is critical, and has zero slack. e. All of the above are true. 20. Which of the following statements regarding CPM networks is true? a. There can be multiple critical paths on the same project, all with different durations. b. The early finish of an activity is the latest early start of all preceding activities. c. The late start of an activity is its late finish plus its duration. d. If a specific project has multiple critical paths, all of them will have the same duration. e. All of the above are true. 21. Activity M on a CPM network has predecessors N and R, and has successor S. M has duration 5. N's late finish is 18, while R's is 20. S's late start is 14. Which of the following is true? a. M is critical and has zero slack. b. M has no slack but is not critical. c. The last start time of S is impossible. d. N is a critical activity. e. S is a critical activity. 22. Which of the following statements concerning CPM activities is false? a. The early finish of an activity is the early start of that activity plus its duration. b. The late finish is the earliest of the late start times of all successor activities. c. The late start of an activity is its late finish less its duration. d. The late finish of an activity is the earliest late start of all preceding activities. e. The early start of an activity is the latest early finish of all preceding activities. 23. The time an activity will take assuming very unfavorable conditions is a. the optimistic time b. the pessimistic time c. the activity variance d. the minimum time e. exactly twice as long as the expected time 24. The expected activity time in PERT analysis is calculated as a. the simple average of the optimistic, pessimistic, and most likely times b. the weighted average of a, m, and b, with m weighted 4 times as heavily as a and b c. the sum of the optimistic, pessimistic, and most likely times d. the sum of the optimistic, pessimistic, and most likely times, divided by six e. the sum of the activity variances, divided by six 25. Which of the following statements regarding PERT times is true? a. The optimistic time estimate is an estimate of the minimum time an activity will require. b. The optimistic time estimate is an estimate of the maximum time an activity will require. c. The probable time estimate is calculated as t = (a + 4m + b).

d. Pessimistic time estimate is an estimate of the minimum time an activity will require. e. Most likely time estimate is an estimate of the maximum time an activity will require. 26. A project being analyzed by PERT has 60 activities, 13 of which are on the critical path. If the estimated time along the critical path is 214 days with a project variance of 100, the probability that the project will take 224 days or more to complete is a. near zero b. 0.0126 c. 0.1587 d. 0.8413 e. 2.14 27. An activity on a PERT network has these time estimates: optimistic = 2, most likely = 5, and pessimistic = 10. Its expected time is a. 5 b. 5.33 c. 5.67 d. 17 e. none of these 28. A local project being analyzed by PERT has 42 activities, 13 of which are on the critical path. If the estimated time along the critical path is 105 days with a project variance of 25, the probability that the project will be completed in 95 days or less is a. -0.4 b. 0.0228 c. 0.3444 d. 0.9772 e. 4.2 29. Analysis of a PERT problem shows the estimated time for the critical path to be 108 days with a variance of 64. There is a .90 probability that the project will be completed before approximately day ______. a. 98 b. 108 c. 109 d. 115 e. 118 30. A project whose critical path has an estimated time of 120 days with a variance of 100 has a 20% chance that the project will be completed before day ______ (rounded to nearest day). a. 98 b. 112 c. 120 d. 124 e. 220

31. If an activity whose normal duration is 13 days can be shortened to 10 days for an added cost of $1,500, the crash cost per period is a. $500 b. $750 b. $1,500 d. $13,000 e. $15,000 32. A network has been crashed to the point where all activities are critical. Additional crashing a. is unnecessary b. is impossible c. is prohibitively expensive d. may require crashing multiple tasks simultaneously 33. Tom is currently applying for graduate job positions. For each application he submits, the probability that it gets short-listed and he gets invited for an interview is 0.01. a.

If he applies for 8 positions, what is the probability that he will not get a single interview? (2 decimal places)

b.

If he applies for 8 positions, what is the probability that he will get at least one interview?

c.

If he applies for n positions, what is the probability that he will get at least one interview?

d.

Hence fine the minimum number of applications he will have to submit to ensure that the probability that he gets at least one interview is greater than 0.9?

34. A company manufactures and sells two models of lamps, L1 and L2. To manufacture each lamp, the manual work involved in model L1 is 20 minutes and for L2, 30 minutes. The mechanical (machine) work involved for L1 is 20 minutes and for L2, 10 minutes. The manual work available per month is 100 hours and the machine is limited to only 80 hours per month. Knowing that the profit per unit is $15 and $10 for L1 and L2, respectively, determine the quantities of each lamp that should be manufactured to obtain the maximum benefit.

35. With the start of school approaching, a store is planning on having a sale on school materials. They have 600 notebooks, 500 folders and 400 pens in stock, and they plan on packing it in two different forms. In the first package, there will be 2 notebooks, 1 folder and 2 pens, and in the second one, 3 notebooks, 1 folder and 1 pen. The price of each package will be $6.50 and $7.00 respectively. How many packages should they put together of each type to obtain the maximum benefit?

36. On a chicken farm, the poultry is given a healthy diet to gain weight. The chickens have to consume a minimum of 15 units of Substance A and another 15 units of Substance B. In the market there are only two classes of compounds: Type X, with a composition of one unit of A to five units of B, and another type, Y, with a composition of five units of A to one of B. The price of Type X is $10 and Type Y, $30. What are the quantities of each type of compound that have to be purchased to cover the needs of the diet with a minimal cost?

37. There is only 600 milograms of a certain drug that is needed to make both large and small pills for small scale pharmaceutical distribution. The large tablets weigh 40 milograms and the small ones, 30 milograms. Consumer research determines that at least twice the amount of the smaller tablets are needed than the large ones and there needs to be least three large tablets made. Each large tablet is sold for a profit of $2 and the small tablet, $1. How many tablets of each type have to be prepared to obtain the maximum profit?...