Ross$$ Hopkins, president of Hopkins$$ Hospitality, has developed the$$ tasks, durations, and predecessor relationships in the following table for building new motels.

$$

Time $($weeks$)$

Immediate

Time $($weeks$)$

Immediate

Activity

a

m

b

$$Predecessor$($s$)$

Activity

a

m

b

$$Predecessor$($s$)$

A

$6$

$9$

$10$

long dash

G

$3$

$3$

$5$

$$C$,$ E

B

$2$

$9$

$24$

A

H

$1$

$1$

$1$

F

C

$8$

$14$

$18$

A

I

$5$

$5$

$5$

F

D

$4$

$6$

$9$

A

J

$4$

$7$

$14$

$$D$,$ G$,$ H

E

$1$

$2$

$4$

B

K

$1$

$1$

$4$

$$I$,$ J

F

$6$

$8$

$21$

$$C$,$ E

Part $2$

$$a$)$ The expected$($estimated$)$ time for activity C is

$$

enter your response here weeks. $($Round your response to two decimal$$ places.$)$

Part $3$

$$b$)$ The variance for activity C is

$$

enter your response here weeks. $($Round your response to two decimal$$ places.$)$

Part $4$

$$c$)$ Based on the calculation of the estimated$$ times, the critical path is

$$

A $-$ C $-$ F $-$ I $-$ K

A $-$ D $-$ J $-$ K

A $-$ B $-$ E $-$ G $-$ J $-$ K

A $-$ B $-$ E $-$ F $-$ I $-$ K

A $-$ B $-$ E $-$ F $-$ H $-$ J $-$ K

A $-$ C $-$ G $-$ J $-$ K

A $-$ C $-$ F $-$ H $-$ J $-$ K

$.$

Part $5$

$$d$)$ The estimated time for the critical path is

$$

enter your response here weeks. $($Round your response to two decimal$$ places.$)$

Part $6$

$$e$)$ The activity variance along the critical path is

$$

enter your response here weeks. $($Round your response to two decimal$$ places.$)$

Part $7$

$$f$)$ Using the standard normal tableLOADING...$,$ the probability that Hopkins Hospitality will finish the project in $36$ weeks or less is

$$

enter your response here. $($Enter as a probability and round your response to three decimal$$ places.$)$