Question: Question 1. (30 Points) A project designed to refurbish a hospital operating theatre consists of activities A,B,C,D,E F, G and ,H, The estimated times (optimistic,

Question 1. (30 Points)

A project designed to refurbish a hospital operating theatre consists of activities A,B,C,D,E F, G and ,H, The estimated times (optimistic, most-likely and pessimistic times) and precedence relationships shown are as shown.

Activity

Immediate Predecessors

Optimistic Time (O)

Most Likely Time (M)

Pessimistic Time (P)

A

-

5

6

7

B

A

10

13

28

C

A

1

2

15

D

A

8

9

16

E

B

25

36

41

F

B,C,D

6

9

18

G

D

7

12

17

H

E,F,G

12

15

24
  1. Construct a network diagram for the refurbishment project (6 Points)
  2. Determine the project critical path and hence the project duration, d (7 Points)
  3. Find the standard deviation of the expected project duration (project duration) (4 Points)
  4. Determine the float of the project activities and interpret
  5. Using the expected duration obtained in (b) and the standard deviation in (c) above, find the probability that the project will be completed in
    1. Between 65 and 75 days (4 Points)
    2. Between 55 and 70 days (6 Points)
    3. Beyond 71 days (3 Points)

Question 1. (30 Points) A project designed toQuestion 1. (30 Points) A project designed toQuestion 1. (30 Points) A project designed to

A project designed to refurbish a hospital operating theatre consists of activities A,B,C,D,E F, G and ,H, The estimated times (optimistic, most-likely and pessimistic times) and precedence relationships shown are as shown. Activity Immediate Optimistic Most Likely Pessimistic Predecessor Time (0) Time (M) Time (P) S A 5 6 7 . A 10 13 28 A 1 2 15 1 D A 8 9 16 E B 25 36 41 F. B,C,D 6 9 18 G D 7 12 17 H E,F,G 12 15 24 Standard Normal Probabilities Table entry Table entry for z is the area under the standard normal curve to the left of z. Z .00 .01 .02 .03 .05 .06 .07 .08 .09 .0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 .0045 .0060 .0080 .0104 .0136 .0174 ,0222 0222 .0281 0201 .0351 ,0003 .0004 .0006 .0009 .0012 .0017 .0023 .0032 .0043 .0057 , .0003 .0004 .0005 .0008 .0011 .0015 .0021 .0028 .0038 .0051 .0068 .0089 .0116 .0150 .0192 .0054 .0075 .0244 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 42 -1.3 -1.2 -1.1 -1.0 0.9 -0.8 -0.7 2 -0.6 -0.5 -0.4 -0.3 -0.2 0.1 -0.0 .0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 0228 .0287 .0359 .0446 .0548 .0668 .0808 POCO .0968 we .1151 .1357 20 .1587 .1841 2119 .2420 2743 .3085 .3446 .3821 .4207 4602 .5000 .0003 .0005 .0006 .0009 .0013 .0018 .0024 0033 .0044 .0059 .0078 .0102 .0132 0170 .0217 .0274 .0344 0427 0526 .0643 0779 .0778 02 .0934 4444 .1112 2014 .1314 .1539 1200 .1788 2061 .2358 2676 .3015 .3372 .3745 4129 4522 4920 .0436 .04 .0003 .0004 .0006 .0008 .0012 .0016 .0023 .0031 .0041 .0055 .0073 .0096 .0125 .0162 .0207 .0262 .0329 0409 .0505 0618 .0749 .0901 076 .1075 1024 .1271 4400 .1492 1534 .1736 .2005 .2296 2611 .2946 .3300 .3669 .4052 .4443 .4840 .0003 .0003 .0004 .0004 0006 0006 ,0008 .0008 .0011 .0011 .0016 .0015 .0022 .0021 .0030 .0029 0040 .0039 .0052 .0071 .0069 .0094 .0091 0122 .0119 .0158 .0154 .0202 .0197 .0256 .0250 .0322 .0314 0401 0392 .0485 0606 .0594 .0721 0885 .0869 .1056 1920 .1038 404 .1251 4990 .1230 20 .1469 .1446 Tror .1711 1685 404 1040 .1977 .1949 20 var 2266 .2236 .2578 .2546 .2912 2877 .3264 .3228 .3632 .3594 4013 .3974 .4404 .4364 .4801 .4761 .0099 .0129 .0166 .0212 ,0268 .0336 0418 .0516 0630 .0764 ,0918 .1093 420 .1292 are .1515 .1762 10 .2033 2007 .2327 .2643 .2981 .3336 3707 .4090 .4483 .0003 .0004 .0005 .0007 .0010 .0014 .0020 .0027 .0037 .0049 .0066 .0087 .0113 .0146 .0188 .0239 .0301 .0375 .0465 0571 .0694 .0838 1002 . 1003 4400 .1190 41 .1401 .1635 .1894 .2177 .2483 .2810 3156 .3520 .3897 .4286 4681 0495 .0002 .0003 .0005 .0007 .0010 .0014 .0019 .0026 .0036 .0048 .0064 .0084 .01 10 .0143 .0183 10) .0233 0294 0294 .0367 .0455 .0559 .0681 .0823 0985 .0985 .1170 4975 . 1379 .1611 2005 .1867 .2148 .2451 .2776 .3121 .3483 .3859 .4247 .4641 0735 .0307 .0384 .0475 ,0582 .0708 .0853 . 1020 .1210 * .1423 .1660 . 1922 02 .2206 co .2514 .2843 .3192 .3557 .3936 4325 .4721 .0537 0655 .0793 ,0951 .1131 4990 .1335 .1562 2012 .1814 .2090 .2389 .2709 .3050 .3409 .3783 .4168 4562 4960 .4880 Standard Normal Probabilities Table entry Table entry for z is the area under the standard normal curve to the left of z 2 Z .00 .01 .02 .03 .04 .06 .07 .08 .09 .5359 .5753 .6141 .6517 .6879 .7224 .7549 .7852 .8133 .8389 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.17 1.5 112 1.6 1.0 1.7 1.8 1.9 10 20 2.0 2.1 2.2 -- 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 .8621 .8830 .9015 .9177 .9319 9441 .9545 .5000 5398 .5793 .6179 .6554 .6915 .7257 .7580 .7881 8159 .8413 .8643 .8849 .9032 .9192 .9332 9452 .9554 .9641 9712 9713 9772 977 0011 .9821 9861 .9893 02 .9918 .9938 9953 .9965 9974 .9981 9987 .9990 .9993 .9995 .9997 .5040 .5438 .5832 .6217 .6591 .6950 .7291 .7611 .7910 .8186 .8438 .8665 .8869 .9049 .9207 .9345 9463 .9564 .9649 9719 .9719 .9778 .9826 .9864 nood 9896 0 19920 .9940 vo .9955 .9966 .9975 .9982 .9987 .9991 .9993 .9995 .9997 .05 .5199 .5596 .5987 .6368 .6736 .7088 .7422 .7734 8023 .8289 .8531 .8749 .8944 .9115 .9265 .9394 .9505 .9599 .9678 .5080 .5478 .5871 .6255 .6628 .6985 .7324 .7642 .7939 .8212 .8461 .8686 .8888 .9066 .9222 .9357 9474 .9573 .9656 9726 .9783 9830 .9868 .9898 0000 .9922 24- .9941 .9956 2 .9967 20% .9976 ero .9982 .9987 .9991 .9994 .9995 9997 .5120 .5517 .5910 .6293 .6664 .7019 .7357 .7673 .7967 .8238 .8485 .8708 .8907 .9082 .9236 .9370 .9484 .9582 .9664 9732 .9788 .9834 00 .9871 2001 .9901 .9925 .9943 21 .9957 .9968 .9977 .9983 .9988 .9991 .9994 .9996 .9997 5160 .5557 5948 .6331 .6700 .7054 .7389 7704 .7995 .8264 .8508 .8729 .8925 .9099 .9251 .9382 2304 9495 .9591 .9671 9738 9738 9792 .9793 9838 .9838 0926 9875 .9904 9004 02- 19927 9945 0 .9959 .9969 ov .9977 .9984 .9988 .9992 .9994 .9996 .9997 .5239 .5636 .6026 .6406 .6772 .7123 .7454 .7764 .8051 .8315 .8554 .8770 .8962 .9131 .9279 .9406 9100 .9515 9608 13006 .9686 9750 .9803 .9846 .9881 .9909 2021 .9931 0020 19948 .9961 024 .9971 .9979 .9985 .9989 .9992 .9994 9996 .9997 .5279 .5675 .6064 .6443 ,6808 .7157 .7486 .7794 .8078 .8340 .8577 .8790 .8980 .9147 .9292 .9418 .9525 .9616 .9693 .9756 .9808 .9850 .9884 04 .9911 .9932 040 19949 .9962 .9972 .9979 9985 .9989 .9992 .9995 .9996 .9997 .5319 .5714 .6103 .6480 6844 .7190 .7517 .7823 .8106 .8365 .8599 .8810 .8997 .9162 .9306 .9429 .9535 9625 .9699 .9761 AR1 9812 .9854 .9887 0045 .9913 .9934 .9951 .9963 9973 .9980 .9986 .9990 .9993 .9995 .9996 .9997 -9633 .9744 .9798 .9842 .9878 .9906 .9929 9946 .9960 .9970 .9978 .9984 .9989 .9992 .9994 .9996 .9997 9706 .9767 .9817 .9857 9890 .9916 .9936 or .9952 ora 19964 .9974 .9981 .9986 .9990 .9993 .9995 .9997 .9998

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