The target time for the completion of an engineering project is 120 days. You ar

Question

The target time for the completion of an engineering project is 120 days. You are considering three engineering firms to complete the project. Having performed similar project to yours in the past, all three firms treat their estimated project completion times as random variables. Project durations for each firm are assumed to be normally distributed with parameters found in the table. What is the probability of a project delay for each of the firms? What firm do you choose to complete the project, and how do you make that choice?

Explanation / Answer

Let M be the mean and sd be the standard deviation

A) Firm A

P(X<120) = P(Z= (X-M)/sd) = P(Z=(120-115)/5.5)

= P(Z= 0.91) = 0.8156

Probability of project delay = 1-0.8156 = 0.1844

Firm B

P(X<120) = P(Z=(120-112)/8.5) = P(z=0.94)

= 0.8264

Probability of project delay of firm B = 1-0.8264 = 0.1736

Firm C

P(X<120) = P(Z=(120-118)/2.5) = P(Z=0.8)

= 0.7881

P(project delay for firm C) = 1-0.7881 = 0.2119

B) I would prefer firm B to complete the project, because the probability of delay is least for firm B

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