Consider the filming of the scene described in Problem 2. Based on past experien

Question

Consider the filming of the scene described in Problem 2. Based on past experience, the director is not very confident about the time estimates for some of the activities. His estimates for the minimum, most likely, and maximum times for these activities are Including these PERT time estimates, how long is the filming expected to take? What is the probability that the filming is completed before 16 days? Before 24 days? How many days are required to complete the filming with probability 0.95? What is the probability that the number of days required to complete the filming of the scene is at least 30 percent larger than the answer you found in part (a)?

Explanation / Answer

Before we start

Now coming to questions

Q1)

The expected time = (time of the critical path A-B-C-F-I-J-K) = 2+4.5 +1.0 +most likely(F-I-J-K)=22.17 days

Q2) P(completed before 16 days)=P(1-(16-22.17)/6.5)=1-0.8264 =0.1736=17.3%

      P(completed before 24 days)=P((24-22.17)/6.5)=0.6103 =61.03%

Q3)P(z-22.17)/6.5)=0.95 thus Z=22.17+6.5*1.645=32.86 = approx 33 days

Q4) Z=130/100*22.17=28.82 days

P((28.82-22.17)/6.5)=0.842 = 84.2 %

note P here represents probability for normal distribution

Activity optimistic average pessimistic E(activity)=(a+4m+b)/6 Var(activity)=(b-a)^2/36 F 2 3 12 4.33 2.78 I 1 2 8 2.83 1.36 J 3 4 10 4.83 1.36 K 1 2 7 2.67 1.00 Most likely 14.67 Standard deviation 6.50

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