Question

A B C D E G H Most Optimistic J $3553105101018$ Most Likely $15881015591512$ Worst Case Time $203624121522825333230$

PERT$-$MEAN $16\mathrm{.}5010\mathrm{.}178\mathrm{.}179\mathrm{.}6715\mathrm{.}335\mathrm{.}0011\mathrm{.}0017\mathrm{.}1715\mathrm{.}00$ SD $21\mathrm{.}335\mathrm{.}503\mathrm{.}171\mathrm{.}172\mathrm{.}002\mathrm{.}001\mathrm{.}003\mathrm{.}333\mathrm{.}833\mathrm{.}67$ Variance $2\mathrm{.}0030\mathrm{.}2510\mathrm{.}03$

$1\mathrm{.}364\mathrm{.}004\mathrm{.}001\mathrm{.}0011\mathrm{.}1114\mathrm{.}6913\mathrm{.}444\mathrm{.}00$ Path Mean $129\mathrm{.}33$ SD $9\mathrm{.}6896279$

Using the data provided answer the following:

Question $1.$ Assume that activity A took $20$ days to complete. Upon completion of activity A$,$ the project planner wants to determine the probability that project will be completed in $80$ day? What is the probability?$$

Question $2.$ Assume that activity A took $20$ days to complete. Activity times for B$,$ D and F remained unchanged but activity C took $10\mathrm{.}2$ days to complete.$$ What is the probability that project will be completed in $80$ days based on project progress at the end of $30\mathrm{.}2$ days?

Question $3.$ Assume that activity A took $16\mathrm{.}5$ days, B $12$ days, F $8$ days, and E $10$ days. Activity times for C and D remained unchanged. What is the probability that project will be completed in $80$ days based on the project progress at the end of $38\mathrm{.}5$ days?$$

Question $4.$ Assume that activities A and B took $16\mathrm{.}5$ and $10\mathrm{.}2$ days, respectively.$$ If activity E takes $17$ days and H takes $20$ days, what is the probability that project will be completed in $80$ days upon completion of activity H$?$ What should be the new activity time for activity J to have probability of completion to be $\mathrm{.}95?$