A project has four activities (A, B, C, and D) that must be performed sequentially. The probability distributions for the time required to complete each of the activities are as follows: Activity Activity Time (weeks) Probability A 5 0.25 6 0.35 7 0.25 8 0.15 B 3 0.20 5 0.55 7 0.25 C 10 0.10 12 0.25 14 0.40 16 0.20 18 0.05 D 8 0.60 10 0.40 (a) Construct a spreadsheet simulation model to estimate the average length of the project and the standard deviation of the project length. Round your answers to one decimal place. Average Project Length weeks Standard Deviation in Project Length weeks (b) What is the estimated probability that the project will be completed in 35 weeks or less

Respuesta :

Answer:

(a)

The average length of the project is 33.9 weeks

The standard deviation of the project length is 2.8 weeks

(b)

The estimated probability that the project will be completed in 35 weeks or less is 0.65

Step-by-step explanation:

(a)

The average length of the project is;

E(P) = E(A+B+C+D)

      = 6.3 + 5.1 + 13.7 + 8.8

      = 33.9

The standard deviation of the project length;

SD(P) = √V(P)

         = √V(A+B+C+D)

         = √1.01 + 1.79 + 4.11 + 0.96

         = √7.87

         = 2.8

(b)

Normal distribution with mean 33.9 weeks and variance of 2.8² weeks.

The estimated probability that the project will be completed in 35 weeks or less is;

[tex]P(P \leq 35) = P( \frac{P-E(P)}{SD(P)} \leq \frac{35-33.9}{2.8} )[/tex]

[tex]P(P \leq 35) = P(z\leq0.3929)[/tex]

                 = 0.65  → Using Excel command (NORM.S.DIST(0.3929,TRUE))

Ver imagen akindelemf