A PERT project is detailed in the table below. Durations are given in days.

Activity Predecessors Optimistic

Pessimistic

Most likely

duration Expectation Variance

duration

duration

A - 23 29 27

B A 46 58 54

C A 22 28 26

D A 30 42 38

E B 23 29 27

F B, C 21 27 25

G C, F 45 63 57

H G 23 29 27

I F, H 28 34 32

J E, I 33 39 37

K F, H, I 24 30 28

a. Draw an activity-on-node network representing this project. (5 points)

b. Give the expected duration and variance of each activity in the table. (5 points)

c. What is the expected duration of the project? (2 points)

d. What is the variance in the project's duration? (3 points)

e. How many days are needed for the project to be 80% likely to be completed? (5 points)

A sample of the standard table for the normal distribution is provided below

Activity Predecessors Optimistic duration Pessimistic duration Most likely duration Expectation Variance NORMAL CURVE AREAS 1.55 Standard deviations Area is 93943 0 1.55 Mean Z TABLE LI Z .0 .1 3 4 .65542 5 .00 .01 .02 04 .05 .06 .07 .08 .09 50000 .50399 50798 51197 51595 51994 52392 .52790 53188 53586 53983 54380 54776 55172 55567 55962 56356 .56749 57142 57535 57926 58317 58706 59095 .59483 59871 60257 .60642 .61026 61409 .61791 .62172 62552 .62930 .63307 .63683 64058 .64431 .64803 65173 66640 .67003 .67364 67724 .68082 .65910 66276 69847 .68439 68793 .69146 .69497 .70194 .70540 .70884 71226 .71566 .71904 72240 .6 .72575 .72907 73237 73565 .73891 74215 74537 74857 .75175 .75490 .7 .75804 .76115 76424 .76730 .77035 77337 77637 77935 .78230 78524 .8 78814 .79103 .79389 .79673 .79955 80234 80511 .80785 .81057 81327 .81594 .81859 82121 82381 .82639 .82894 83147 .83398 .83646 83891 1.0 .84134 .84375 84614 84849 .85083 85314 85543 .85769 .85993 86214 1.1 .86433 .86650 86864 .87076 .87286 .87493 87698 .87900 .88100 88298 1.2 .88493 .88686 88877 .89065 .89251 89435 89617 .89796 .89973 90147 1.3 .90320 90490 90658 90824 .90988 91149 91309 .91466 .91621 91774 1.4 91924 92073 92220 92364 .92507 92647 92785 92922 .93056 93189 1.5 .93319 93448 93574 93699 93822 93943 94062 94179 94295 94408 1.6 94520 94630 94738 94845 94950 95053 95154 95254 95352 95449 1.7 .95543 95637 95728 95818 .95907 95994 96080 .96164 .96246 96327 1.8 96407 96485 96562 96638 .96712 96784 96856 .96926 .96995 97062 1.9 97128 97193 97257 97320 97381 97441 97500 97558 97615 97670 2.0 97784 97831 97932 97982 98030 98077 98124 98169 97725 97882 2.1 .98214 98257 98300 98341 98382 98422 98461 98500 .98537 98574 2.2 98610 98645 98679 98713 .98745 98778 98809 98840 98870 98899 2.3 98928 98956 98983 99010 .99036 .99061 99086 99111 99134 99158 2.4 .99180 99202 99224 99245 .99266 99286 99305 99324 .99343 99361 2.5 .99379 99396 99413 99430 .99446 99461 99477 99492 .99506 99520 2.6 .99534 99547 99560 99573 .99585 99598 99609 99621 99632 99643 2.7 .99653 .99664 99674 99683 .99693 99702 99711 99720 .99728 99736 2.8 .99744 99752 99760 99767 .99774 99781 99788 99795 .99801 99807 2.9 .99813 99819 99825 99831 .99836 99841 99846 .99851 99856 99861 3.0 99865 99874 99878 .99882 99886 99889 99893 .99896 99900 .99869 .99906 99910 3.1 .99903 99913 .99916 99918 99921 99924 .99926 99929 3.2 .99931 99934 99936 99938 .99940 99942 99944 99946 .99948 99950 3.3 .99952 99953 99955 99957 .99958 99960 99961 99962 .99964 99965 3.4 99966 .99968 99969 99970 99971 99972 99973 99974 .99975 99976 3.5 .99977 .99978 99978 99979 .99980 99981 99981 .99982 .99983 99983 3.6 99984 99985 99985 99986 99986 99987 99987 99988 .99988 99989 3.7 99989 99990 99990 99990 99991 99991 99992 99992 99992 99992 3.8 99993 .99993 99993 99994 .99994 99994 99994 .99995 .99995 99995 3.9 99995 99995 99996 99996 99996 99996 99996 99996 99997 99997