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.

Firm i

µi

i

A

115

5.5

B

112

8.5

C

118

2.5

a) What is the probability of a project delay for each of the firms?

b) What firm do you choose to complete the project, and how do you make that choice?

Firm i

µi

i

A

115

5.5

B

112

8.5

C

118

2.5

Explanation / Answer

THE ESTIMATED TIME OF COMPLETION IS 120

IF ANY COMPANY TAKES MORE THEN THAT THEN IT WILL BE A DELAY

WE NEED TO CALCULATE THE PROBABILITY OF DELAY FOR EACH COMPANY

FOR COMPANY A, MEAN = 115, STANDARD DEV = 5.5

P(X>120) For x = 120, z = (120 - 115) / 5.5 =0.90

Hence P(x > 120) = P(z > 0.90) = [total area] - [area to the left of 0.90]

= 1 - 0.8159 = 0.1841

FOR COMPANY B, MEAN = 112, STANDARD DEV = 8.8

P(X>120) =  For x = 120, z = (120 - 112) / 8.5 =0.94

Hence P(x > 120) = P(z > 0.94) = [total area] - [area to the left of 0.94]

= 1 - 0.8264 = 0.1735

FOR COMPANY C, MEAN = 118, STANDARD DEV = 2.5

P(X>120) =  For x = 120, z = (120 - 118) / 2.5 =0.8

Hence P(x > 120) = P(z > 0.80) = [total area] - [area to the left of 0.80]

= 1 - 0.7881 = 0.2119

B) NIW THE FIRM WHICH HAS THE LEAST PROBABILITY OF HAVING THE DELAY WILL BE PICKED UP AS A CHOICE AND AS PER THE CALCULATION ABOVE THE COMPANY WITH LEAST PROBABILITY OF DELAY IS COMPANY B.

hence the choice will be company b

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.