The following$$ table represents a plan for a project: Use Appendix G$.$

TIMES $($DAYS$)$

JOB NO$.$ PREDECESSOR

JOB$($S$)$ a m b

$1138$

$21336$

$313612$

$415712$

$523612$

$63123$

$742910$

$85,6246$

$982412$

$107447$

$119,1021111$

b$.$ Indicate the critical path.

multiple choice $1$

$1-3-6-8-9-11$

$1-2-5-8$

$1-4-7-10-11$

$1-2-5-8-9-11$

c$.$

What is the expected completion time for the project? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Expected completion time

$33$

days

d$.$

You can accomplish any one of the following at an additional cost of $$2,000.$ If you will save $$1,500$ for each day that the earliest completion time is reduced, which of the following actions should be taken, if any?

$1.$ Reduce job $6$ by two days.

multiple choice $2$

Yes

No

$2.$ Reduce job $4$ by two days.

multiple choice $3$

Yes

No

$3.$ Reduce job $9$ by two days.

multiple choice $4$

Yes

No

e$.$

What is the probability that the project will take more than $35$ days to complete? $($Use Excel's NORMSDIST$()$ function to find the correct probability for your computed Z$-$value. Do not round intermediate calculations. Round $"$z$"$ value to $2$ decimal places and final answer to $4$ decimal places.$)$

Probability