Question: Section 1 Consider a small project that involves the following activities: Project Tasks Preceding Task(s) Start A B D E End Start Start A B,

Section 1 Consider a small project that involves

Section 1 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) 2 Z .05 1.2 The Cumulative (Single Tail) Probabilities of the Normal Probability Distribution (Areas under the Normal Curve from - co to z). 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 .04 column. At the intersection read .9099. The area to the right of 2 = 1.34 is 1 - 9099 = .0901. The area between the mean (dashed line) and 2 = X 1.34 = 9099 - 5 = 4099. 00 .01 .02 .03 .04 .06 .07 .08 .09 .0 .5000 .5040 5080 5120 5160 .5199 5239 .52795319 5359 .1 .5398 .5438 5478 5517 5557 .5596 5636 .5675 .5714 5753 .2 5793 58325871 .5910 5948 5987.6026 .6064 6103.6141 3 .6179.6217 .6255 .6293 .6331.6368.6406 .6443.6480.6517 .4 .6554 .6591.6628 .6664 .6700 .6736 6772 6808 .6844 .6879 .5 .6915 .6950.6985.7019 .7054 .7088 7123 .7157 .7190.7224 .6 .7257 .7291 .7324 .7357.738974227454 .7486 .7517.7549 .7 .7580 .7611 7642 7673.7704 7734 7764 7794 .7823.7852 .8 .7881 .7910 7939.79677995.8023 8051 .8078 .8106 .8133 .9 .8159 .8186 .8212 .8238.8264 82898315 8340.8365.8389 1.0 .8413.8438 8461 .8485.8508 .8531 8554 .8577 .85998621 1.1 .8643.8665 .8686 8708 .8729 .87498770 .8790 .8810 8880 .8849 .8869.8888 .89078925 8944 8962_8980 .89979015 1.3 9032 90499066 9082 9099 9115 9131 .9147 .9162 9177 1.4 9192 .92079222 9236 9251 9265 9276 .9292 .9306 9319 1.5 .9332 9345 9357 9370 938293949406 9418 94299441 1.6 9452 94639474 9484 .9495 9505 9515 9525 .9535 9545 1.7 9554 9564 9573 9582 9591 95999608 .9616 .9625 9633 1.8 .9641 .9649 9656 .9664 9671 .9678 9686 969396999706 1.9 97139719 9726 9732 9738 .9744 9750 9756 9761 9767 2.0 .9772 9778 97839788 9793 .9798 9803 .9808 .9812 9817 2.1 9821 9826 9830 9834 9838 .9842 9846 .9850 9854 9857 2.2 9861 9864 98689871 .9875 .9878 9881 9884 9887 9890 2.3 9893 9896 9898 .9901 .9904 .9906 9909 .9911 9913 9916 2.4 .9918 9920 9932 9925 .9927 .99299931 9932 9934 9936 2.5 .9938 9940 9941 .99439945 .9946 9948 .99499951 9952 2.6 .9953 9955 9956 9957 9959 .9960 9961 99629963 9964 2.7 9965 9966 9967 .9968 .9969 .9970 9971 99729973 9974 2.8 .9974 9975 9976 9977 .9977 .9978 9979 99799980 9981 .9981 9982 99829983 .9984 .9984 9985 9985 9986 9986 3.0 .9987 99879987 9988 .9988 .9989998999899990 9990 3.1 .9990 9991 9991 9991 .9992 .9992 99929992 99939993 3.2 .99939993 9994 9994 9994 .9994 9994 9995 9995 9995 3.3 .9995 9995 9995 9996 .9996 .9996 9996 9996 9996 9997 3.4 .9997 9997 99979997 99979997 999799979997 9998 2.9

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