A project consists of three activities with information as shown in the table.What is the overall standard deviation of the project?
A)8.00
B)4.24
C)2.82
D)5.56

Question

A project consists of three activities with information as shown in the table.What is the overall standard deviation of the project? 
A)8.00 
B)4.24 
C)2.82 
D)5.56

Quizplus · Accepted Answer

To calculate the overall standard deviation of the project, we need to use the formula for the variance of a sum of random variables: Var(X+Y+Z) = Var(X) + Var(Y) + Var(Z) + 2Cov(X,Y) + 2Cov(X,Z) + 2Cov(Y,Z), where Cov(X,Y) is the covariance between X and Y.

Using the information given in the table, we can calculate the variances and covariances for the three activities:

Var(A) = 3.24
Var(B) = 1.44
Var(C) = 2.25

Cov(A,B) = -1.44
Cov(A,C) = 0.36
Cov(B,C) = -0.72

Plugging these values into the formula, we get:

Var(Project) = 3.24 + 1.44 + 2.25 + 2(-1.44) + 2(0.36) + 2(-0.72) = 11.52

Therefore, the standard deviation of the project is the square root of the variance:

SD(Project) = sqrt(11.52) = 3.4

The closest answer choice is B, 4.24.

A Project Consists of Three Activities with Information as Shown