{Exercise 4.17} Refer to the KP&L sample points and sample point probabilities i
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Question
{Exercise 4.17}
Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3.
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.
SelectPoints (3,6), (3,7), and (3,7)Points (4,6), (4,7), and (4,8)Points (2,6), (2,8), and (3,6)Item 1
What is the probability that the design stage is over budget (to 2 decimal)?
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.
SelectPoints (2,8), (3,7), and (3,8)Points (3,6), (3,7), and (3,8)Points (2,8), (3,8), and (4,8) Points (2,6), (2,8), and (3,6)Item 3
What is the probability that the construction stage is over budget (to 2 decimals)?
What is the probability that both stages are over budget (to 2 decimals)?
{Exercise 4.17}
Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3.
TABLE 4.2 COMPLETION RESULTS FOR 40 KP&L PROJECTS Completion Time (months) Stage 1Design Stage 2
Construction Sample point Number of
Past Projects
Having These
Completion Times 2 6 ( 2, 6) 4 2 7 ( 2, 7) 4 2 8 (2, 8) 4 3 6 (3, 6) 2 3 7 (3, 7) 6 3 8 (3, 8) 2 4 6 (4, 6) 4 4 7 (4, 7) 2 4 8 (4, 8) 12 Total 40 Table 4.3 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)=4/40=0.1 (2, 7) 9 months P(2, 7)=4/40=0.1 (2, 8) 10 months P(2, 8)=4/40=0.1 (3, 6) 9 months P(3, 6)=2/40=0.05 (3, 7) 10 months P(3, 7)=6/40=0.15 (3, 8) 11 months P(3, 8)=2/40=0.05 (4, 6) 10 months P(4, 6)=4/40=0.1 (4, 7) 11 months P(4, 7)=2/40=0.05 (4, 8) 12 months P(4, 8)=12/40=0.3 Total 1.00
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.
SelectPoints (3,6), (3,7), and (3,7)Points (4,6), (4,7), and (4,8)Points (2,6), (2,8), and (3,6)Item 1
What is the probability that the design stage is over budget (to 2 decimal)?
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.
SelectPoints (2,8), (3,7), and (3,8)Points (3,6), (3,7), and (3,8)Points (2,8), (3,8), and (4,8) Points (2,6), (2,8), and (3,6)Item 3
What is the probability that the construction stage is over budget (to 2 decimals)?
What is the probability that both stages are over budget (to 2 decimals)?
Explanation / Answer
BY Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3,
we can see that three sample points in the event the design stage is over budget and the sample points include
(4, 6), (4, 7), (4, 8).
the probability that the design stage is over budget is as follow:
P(4, 6)+P(4, 7)+P(4, 8)=0.05+0.10+0.15=0.30
Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3,
we can see that three sample points in the event the design stage is over budget and the sample points include
(2, 8), (3, 8), (4, 8).
the probability that the construction stage is over budget is as follow:
P(2, 8)+P(3, 8)+P(4, 8)=0.05+0.05+0.15=0.25
Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3,
we can find that there is only one sample point-(4, 8) that both stages are over budget. Therefore, we can compute the probability that both stages are over budget is P(4, 8)=0.15
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