Consider a small project that involves the following activities: Activity Immediate Completion Times (days) predecessors Optimistic Most Likely A None 3 6 B None 12 18 9 12 D C 15 18 B 9 18 Pessimistic 9 24 15 21 15 Required: (a) (b) Determine the expected value (mean) and the variance of the completion time for each activity. Assuming that the normal distribution applies, determine the probability that the project will take 36 or less days to complete. Assuming that the normal distribution applies, determine the project time for which the probability that we can complete the project is at least 80%. TABLE A Areas of a Standard Normal Distribution (Alternate Version of Appendix I Table 4) The table entries represent the area under the standard normal curve from O to the specified value of 2. 2 .00 .01 .02 .03 .04 .05 06 07 08 09 0.0 .0000 .0040 .0080 .0120.0160.01990239 0279.0319 .0359 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 0675 0714 0753 0.2 .0793 .0832 0871 0910 0948 0987 1026 1064 1103 1141 0.3 .1179 1217 1255 12931331 1368 1406 1443 .1480 1517 0.4 .1554 .1591 .1628 .1664 1700 1736 1772 .1808 1844 1879 0.5.1915 1950 1985 .2019.2054 2088 2123 2157 2190 2224 0.6 .2257 2291 2324 2357 2389 2422 2454 2486 2517 2549 0.7 2580 2611 2642 2673 2704 2734 2764 2794 2823 2852 0.8 2881 2910 2939 2967 2995 3023 3051 3078 3106 3133 0.9 .31593186 3212 3238 3264 3289 3315 3340 3365 3389 1.0 3413 3438 3461 34853508 3531 3554 3577 3599 3621 1.1.3643 3665 3686 3708 37293749 3770 3790 3810 3830 1.2 384938693888 3907 3925 3944 3962 3980 3997 4015 1.3 .4032 4049 4066 4082 4099 4115 4131 41474162 4177 1.4 .4192 42074222 4236 4251 42654279429243064319 1.5 .43324345 4357 4370 43824394 4406 4418 44294441 1.6 .4452 4463 4474 4484 44954505 4515 4525 4535 4545 1.7 .4554 4564 4573 4582 4591 4599 4608 4616 4625 4633 1.8 4641 4649 4656 4664 4671 4578 4686 469346994706 1.9.4713 4719 4726 4732 4738 4744 4750 4756 4761 4767 2.0 .4772 4778 4783.4788 4793 4798 4803 4808 48124817 2.1.4821 4826 4830 4834 4838 4842 4846 4850 4854 4857 2.2.4861 4864 4868 4871 48754878 4881 4884 4887 4890 4893 4896 4898 4901 4904 49064909 4911 4913 4916 .4918 4920 4922.4925 4927 4929 4931 4932 4934 4936 4938 49404941 4943 494549464948 4949 4951 4952 2.6 .4953 4955 4956 4957.4959.49604961 4962 1963 4964 2.7 .4965 49664967496849694970 1971 1972 49734974 2.8 .4974 4975 4976 4977 4977 4978 49794979 49804981 2. 9 4981 4982 4982 4983 4984 4984 4985 4985 4986 4986 3.0.4987 4987 4987 4988 49884989498949894990 4990 3.1.4990 4991499149914992 4992 4992 4992 49934993 3.2.499349934994 4994 4994 4994 4994 4995 4995 4995 3.3.4995 4995 4995.4996 4996 4996 4996 4996 4996 4997 3.4.4997 4997 4997 4997 4997 4997 4997 4997 4997 4998 3.5 4998 4998 4998 4998 4998 4998 4998 4998 4998 4998 3.6 .4998 4998 4998 4999.4999.4999 4999 4999 4999 4999 For values of greater than or equal to 3.70, use 0.4999 to approximate the shaded area under the standard normal curve. 2.5
