Refer to the KP&L sample points and sample point probabilities in the following tables.

Completion Results for 40 KP&L Projects Completion Time (months) Sample

Point Number of

Past Projects

Having These

Completion Times Stage 1

Design Stage 2

Construction 2 6 (2, 6) 6 2 7 (2, 7) 4 2 8 (2, 8) 4 3 6 (3, 6) 2 3 7 (3, 7) 8 3 8 (3, 8) 6 4 6 (4, 6) 6 4 7 (4, 7) 2 4 8 (4, 8) 2

Total: 40

Probability Assignments for the KP&L Project Based on the Relative Frequency Method Sample

Point Project

Completion Time Probability of

Sample Point (2, 6) 8 months P(2, 6) =640= 0.15

(2, 7) 9 months P(2, 7) =440= 0.10

(2, 8) 10 months P(2, 8) =440= 0.10

(3, 6) 9 months P(3, 6) =240= 0.05

(3, 7) 10 months P(3, 7) =840= 0.20

(3, 8) 11 months P(3, 8) =640= 0.15

(4, 6) 10 months P(4, 6) =640= 0.15

(4, 7) 11 months P(4, 7) =240= 0.05

(4, 8) 12 months P(4, 8) =240= 0.05

Total: 1.00

(a)

The design stage (stage 1) will run over budget if it takes 4 months to complete. List the sample points in the event the design stage is over budget. (Select all that apply.)

• (2, 6)
• (3, 6)
• (4, 6)
• (2, 7)
• (3, 7)
• (4, 7)
• (2, 8)
• (3, 8)
• (4, 8)

(b)

What is the probability that the design stage is over budget?

(c)

The construction stage (stage 2) will run over budget if it takes 8 months to complete. List the sample points in the event the construction stage is over budget. (Select all that apply.)

• (2, 6)
• (3, 6)
• (4, 6)
• (2, 7)
• (3, 7)
• (4, 7)
• (2, 8)
• (3, 8)
• (4, 8)

(d)

What is the probability that the construction stage is over budget?

(e)

What is the probability that both stages are over budget?