Problem $17-7$

Three recent college graduates have formed a partnership and have opened an advertising firm. Their first project consists of activities listed in the following table. Use Table B$.$

TIME IN DAYS

Activity Immediate Predecessor Optimistic Most Likely Pessimistic

A $567$

B $8811$

C A $6811$

D $91215$

E C $569$

F D $567$

G F $237$

H B $445$

I H $578$

End E$,$ G$,$ I

b$.$

What is the probability that the project can be completed in $24$ days or less? In $21$ days or less? $($Round your te and z values to $2$ decimal places and "Standard deviation" to $3$ decimal places. Round your final answers to $4$ decimal places.$)$

Days Probability

$24$ days or less

$\mathrm{.}9677$

$21$ days or less

$\mathrm{.}2349$

c$.$

Suppose it is now the end of the seventh day and that activities A and B have been completed while activity D is $50$ percent completed. Time estimates for the completion of activity D are $5,6,$ and $7.$ Activities C and H are ready to begin. Determine the probability of finishing the project by day $24$ and the probability of finishing by day $21.($Round your intermediate calculations to $3$ decimal places and final answers to $4$ decimal places.$)$

Probability

Day $24$

Day $21$