The XYZ Company is considering a recreation project to enable the company to begin new financial projects. The company's president must determine whether to make the expansion a small, medium- or large-scale project. Human resource's salaries for the new financial projects is uncertain, which may be low salary, medium salary, or high salary. The probability estimates for salaries are .30, .45, and .25, respectively. Letting x,y and z indicate the annual cost in thousands of dollars, the firm's human resource has for the small, medium- and large-scale expansion projects.
a. Expected cost :
Low scale i.e. E(X) = 35*0.3 + 65*0.45 + 82*0.25 = 60.25
E(Medium scale) = 42*0.3 + 68*0.45 + 90*0.25 = 65.7
E(Large scale) = 50*0.3 + 75*0.45+ 110*0.25 = 76.25
cost is minimum for low scale
b. variance :
Vx = E(X2) - E(X)2 = 3949.75 - 3630.0625 = 319.69
Vy = 4635 - 4316.49 = 318.51
vz = 6306.25 - 5814.0625 = 492.19