Porcelain figurines are sold for 12 if flawless and for 8 if

Porcelain figurines are sold for $12 if flawless, and for $8 if there are minor cosmetic flaws. Of the figurines made by a certain company, 92% are flawless and 8% have minor cosmetic flaws. In a sample of 100 figurines that are sold, let Y be the revenue earned by selling them and let X be the number of them that are flawless. Find _Y.

Solution

Y = 12 X + 8(100-X) = 12 X + 800 - 8X = 4X + 800 => Y = 4X+800
Mean ( np ) =92
V(X) = Standard Deviation ( Sqrt(npq) )= Sqrt(100*0.92*0.08) = 2.7129
Varaince (Y) = Var[ 4X + 800 ] = 4 * Var(X) = 4 * 2.7129 = 10.8516