Using PERT, Harold Benson was able to determine that the expectedproject complet

Question

Using PERT, Harold Benson was able to determine that the expectedproject completion time for the construction of a pleasure yacht is22.5 months and the project variance is 9.

What is the probability that the project will be completed in 19months?

Round your answer to 3 decimal places; for example, .123.

What is the probability that the project will be completed in 25months?

Round your answer to 3 decimal places; for example, .123.

Using PERT, Harold Benson was able to determine that the expectedproject completion time for the construction of a pleasure yacht is22.5 months and the project variance is 9.

(a)

What is the probability that the project will be completed in 19months?

Round your answer to 3 decimal places; for example, .123.

(b)

What is the probability that the project will be completed in 25months?

Round your answer to 3 decimal places; for example, .123.

Explanation / Answer

Mean: 22.5 Variance: 9 Standard deviation: 3 Assume a normal distribution here. a) P(X < 19) = P(Z < (19-22.5)/3) = P(Z < -1.167) = 0.122= 12.2% The probabilities are obtained from a standard normal table, suchas the one available here: http://www.ul.ie/podgorski/Teaching/Business/Handouts/normal01.jpg Since we cannot find -1.167 on the table, given the symmetricnature of the normal distribution, find P(Z > 1.167) = 1 - P(Z< 1.167) = 1 - 0.878 = 0.122 b) P(X < 25) = P(Z < (25-22.5)/3) = P(Z < 0.8333) = 0.798= 79.8%

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