Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and
ID: 2930690 • Letter: R
Question
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.
What is the probability that the design stage is over budget (to 2 decimals)?
The construction stage (stage 2) will run over budget if it takes 9 months to complete. List the sample points in the event the construction stage is over budget.
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)?
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 7 ( 2, 7) 4 2 8 ( 2, 8) 6 2 9 (2, 9) 2 3 7 (3, 7) 4 3 8 (3, 8) 6 3 9 (3, 9) 2 4 7 (4, 7) 2 4 8 (4, 8) 2 4 9 (4, 9) 12 Total 40
Explanation / Answer
Solution:
(a)
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, 7), (4, 8) ,(4, 9).
(b)
The probability that the design stage is over budget = (Number of projects where the design stage is over budget)/(Total number of projects) = (2 + 2 + 12)/40 = 0.05 + 0.05 + 0.3 = 0.4
(c)
The construction stage (stage 2) will run over budget if it takes 8 months to complete. The sample points in the event the design stage is over budget are (2,9), (3,9), and (4,9)
(d)
The probability that the construction stage is over budget = (Number of projects where the construction stage is over budget)/(Total number of projects) = (2 + 2 + 12)/40 = 0.05 + 0.05 + 0.3 = 0.4
(e)
Probability that both stages are over budget:
we can find that there is only one sample point-(4, 9) that both stages are overbudget. Therefore, we can compute the probability that both stages are over budget is P(4, 9)=12/40=0.3