You may need to use the appropriate technology to answer this question.

A project consists of five activities as shown in the following table.

Activity	Optimistic Time (hr)	Most Probable Time (hr)	Pessimistic Time (hr)
Floor sanding	4	5	6
Floor buffing	3	4	5
Paint mixing	0.5	1	1.5
Wall painting	3	4	11
Ceiling painting	2	6.5	8

Naturally, the paint mixing precedes the painting activities. Also, both ceiling painting and floor sanding must be done prior to floor buffing.

(a)

Construct the PERT/CPM network for this problem.

A project network with 7 activities and 8 directed arcs is shown.

• Activity Start is connected to activity Floor Sanding and to activity Paint Mixing.
• Activity Floor Sanding is connected to activity Floor Buffing.
• Activity Paint Mixing is connected to activity Paint Wall and to activity Paint Ceiling.
• Activity Paint Wall is connected to activity Finish.
• Activity Paint Ceiling is connected to activity Finish.
• Activity Floor Buffing is connected to activity Finish.
• Activity Finish has no arcs directed to other activities.

(b)

What is the expected completion time (in hours) of this project?

hr

(c)

What is the probability that the project can be completed within thirteen hours? (Round your answer to four decimal places.)