For a project, the expected project completion time and its variance have been e

Question

For a project, the expected project completion time and its variance have been estimated as T,- 81 days, and V,-25. Compute the following: (a) the probability that the project can be completed in 78 days, (b) the probability that the project can be completed in 81 days, (c) the probability of completing the project between 78 and 84 days inclusive, and (d) how far ahead the project should be started for a 0.997 probability of completing by the deadline. Refer to the standard normal table for this problem

Explanation / Answer

a) Te = 81 , X = 78 , Va = 25, Standard deviation = Sqrt(Va) = 5

Z = (X-Te) / Std. Deviation = (-3/5) = -0.60 , For Z = 0.60, probability = 0.2743

b) Z = (X-Te) / Std. Deviation = (81-81)/5 = 0 , For Z = 0 , probability = 0.5000

c) Probability of completing project within 84 days.

Z = (X-Te) / Std. Deviation = (84-81)/5 = 0.6 For Z 0.6 , p= 0.7257

For 78-84 , p = 0.7257 - 0.2743 = 0.45

d) Z = (X-Te) / Std. Deviation, For p =0.997 , Z = 2.83

X - 81 = 5*2.83

X= 81+14.15 = 95 days

OR X = Te + Z*standard deviation = 95 days

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