The following table represents a plan for a project:

JOB NUMBER PREDECESSOR JOB$($S$)$ TIMES $($DAYS$)$

a m b

$1234$

$21123$

$314512$

$413411$

$52135$

$63123$

$74189$

$85,6246$

$982412$

$107345$

$119,10578$

b$.$ Indicate the critical path.

multiple choice $1$

$1-4-7-10-11$

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

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

c$.$ What is the expected completion time for the project?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

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

Reduce job $5$ by two days.

multiple choice $2$

Yes

No

Reduce job $3$ by two days.

multiple choice $3$

Yes

No

Reduce job $7$ by two days.

multiple choice $4$

Yes

No

e$.$ What is the probability that the project will take more than $30$ days to complete?

Note: Use Excel's NORMSDIST$()$ function to find the correct probability for your computed Z$-$value. Other than the expected completion time you entered in part c above, do not round intermediate calculations. Round $"$z$"$ value to $2$ decimal places and your final answer to $4$ decimal places