Question: Question 2 Consider a small project that involves the following activities: Project Tasks Preceding Task(s) Start A B D E End Start Start A B,

Question 2 Consider a small project that involves

Question 2 Consider a small project that involves the following activities: Project Tasks Preceding Task(s) Start A B D E End Start Start A B, C A D, E Completion times (days) : Optimistic Most Likely Estimate Duration 0 0 5 6 4 5 4 15 3 4 5 16 0 0 Pessimistic Estimate 0 7 18 20 5 18 0 Questions: (a) Draw the PERT chart. Determine the expected value and the variance of the completion time for each activity. (10 marks) (b) Use the expected times from (a) to find the critical path. (5 marks) (c) Assuming that the normal distribution applies, determine the probability that the critical path will take between 18 and 26 days to complete. (8 marks) (d) How much time must be allowed to achieve a 90% probability of timely completion? (7 marks) M 5040 5948 6664 .7852 The Cumulative (Single Tail) Probabilities of the Normal Probability Distribution (Areas under the Normal Curve from - to 2). Example: the area to the left of 2 = 1.34 is found by following the left 2 column down to 13 and moving right to the 4 column. At the intersection read 9099. The area to the right of Z134 is 1 - 9099 - 0901. The area between the mean (dashed line) and 2 - X 1.349099-54099. z 00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0 .5000 5080 .5120 5160 5199 5239 .5279 5319 5359 .1 5398 5438 5478 .5517 5557 5596 5636 .5675 5714 5753 5793 5832 5871 .5910 5987 .6026 .6064 .6103 .6141 3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 6480 .6517 .4 .6554 .6591 .6628 .6700 .6736 .6772 .6808 .6844 .6879 .5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190.7224 .6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 .7 .7580 .7611 .7642 .7673 .7704 -7734 .7764 .7794 .7823 .8 .7881 .7910 -7939 .7967 -7995 8023 .8051 .8078 .8106 .8133 .9 .8159 .8166 8212 .8238 .8264 8289 8315 .8340 .8365 .8399 .8413 .8438 .8461 .8485 .8508 8531 .8554 .8577 .8599 .8621 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830 1.2 .8849 .8869 .8989 .8907 .8925 .8944 8962 8980 .89979015 13 9032 9049.9066 9082 .9099 9115 9131 9147 9162 .9177 1.4 9192 9207 9222 .9236 .9251 .9265 9276 .9292 .9306 .9319 1.5 9332 93459357 9370 .9382 9994 9406 .9418 .9429 .9441 1.6 9452 94639474 9484 9495 9505 9515 9525 9535 9545 1.7 9554 -9564 9573 9582 9591 .9599 9608 .9625 9633 1.8 964! 9649 9656 .9664 .9671 9678 9686 .9693 .9699 9706 1.9 9713 9719 9726 .9732 .9738 9744 9750 .9756 .9761 .9767 2.0 9772 9778 9783 9788 .9793 9798 .9803 .9808 .9812 9817 2.1 19821 .9826 9830 9834 .9838 9842 .9846 9850 9854 2.2 9857 .9861 .9864 9868 19871 .9875 .9878 .9881 9884 9887 .9890 23 .9893 .9896 9898 .9901 .9904 .9906 .9909 9911 .9913 9916 2.4 .9918 .9920 9932 .9925 .9927 9929 .9931 .9932 .9934 .9936 2.5 9938 9940 9941 .9943 9945 .9946 9948 .9949 .9951 9952 2.6 9953 .9955 9956 .9957 9959 .9960 9961 .9962 .9963 .9964 2.7 9965 9966 9967 .9968 .9969 -9971 9972 .9973 .9974 2.8 9974 9975 9976 .9977 .9977 .9978 9919 9979 .9980 .9981 2.9 .9981 .9982 9982 .9983 .9984 .9984 9985 9985 .9986 .9986 3.0 .9987 9987 9987 9988 .9988 9989 .9989 9999 .9990 3.1 9990 .9990 9991 9991 .9991 .9992 .9992 .9992 9992 9993 .9993 3.2 .9993 9993 9994 .9994 9994 .9994 .9994 9995 .9995 9995 3.3 9995 .9995 9995 .9996 .9996 .9996 .9996 9996 .9996 9997 3.4 -9997 .9997 9997 .9997 .9997 .9997 .9997 9997 .9997 .9998 9616 .9970

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