The duration of a construction project is modeled as a norma

The duration of a construction project is modeled as a normal random variable. The mean duration is 90 da and the corresponding COV 0.25. Compute the probability that the project will be delayed, if the target time for the completion of the project is 100 da. With improved workmanship, the COV can be reduced to 0.15. With the same duration, compute the target time if the accepted probability of delay is 0.10.

Solution

X = duration of construction project

cov(x) = var(x) = 0.25

std dev =0.5

X is normal (90, 0.5)

a) Prob that X>100

= P(Z>10/0.5) = P(Z>20) =0.0000

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b) When cov =0.15

std dev =0.3873

P(X>100+0.1(100))

=P(X>110) = P(Z>133.33)

=0.0000