A project manager has compiled a list of major activities that will be required to install a computer information system in her firm. The list includes estimated completion times for activities and precedence relationships.

Use Table B$1$ and Table B$2.$

Activity Immediate

Predecessor Estimated Times

$($weeks$)$

A $2-4-6$

D A $6-8-10$

E D $7-9-12$

H E $2-3-5$

F A $3-4-8$

G F $5-7-9$

B $2-2-3$

I B $2-3-6$

J I $3-4-5$

K J $4-5-8$

C $5-8-12$

M C $1-1-1$

N M $6-7-11$

O N $8-9-13$

End H$,$ G$,$ K$,$ O

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a$.$ Determine the mean and standard deviation for each of the following paths in the project. $($Round Mean and Standard Deviation to $2$ decimal places.$)$

b$.$ If the project finishes within $26$ weeks of its start, the project manager receives a $$1,000$ bonus. What is the probability of a $$1,000$ bonus? $($Round z$-$value to $2$ decimal places, and probability to $4$ decimal places.$)$

c$.$ If the project finishes within $27$ weeks of its start, the project manager receives a $$500$ bonus. What is the probability of a $$500$ bonus? $($Round z$-$value to $2$ decimal places, and probability to $4$ decimal places.$)$