3.7.6, pp 186-190. (i) A produce department at a local supermarket sells three s

Question

3.7.6, pp 186-190. (i) A produce department at a local supermarket sells three sizes of fruit bas- small, medium, and large. This holiday season, the manager expects kets, to sell 25 small, X, 18 medium, Y, and 9 large baskets, Z. If the de- partment makes a profit of $5 for each small basket, $8 for each medium basket, and $10 for each large basket, find the expected total profit, E(5X +8Y+102). (ii) A girl randomly cuts rectangles out of a piece of paper in such a way that the length of the long side, X, has a variance of 22 in2, the length of the short side, Y, has a variance of 0.52 in2, and the lengths of the sides are independent. Find the variance of the perimeter of the resulting rectangles, Var(2X +2y). 0300 00 16 360 00 8.5 none of these 01359 00 17 359 (0425 10 poin

Explanation / Answer

i) exepected total profit =E(5X+8Y+10Z) =5E(X)+8E(Y)+10E(Z) =5*25+8*18+10*9=$359

ii)Var(2X+2Y) =22Var(X)+22Var(Y) =4*4+4*0.25=17

option (i) 359 (ii)_ 17 is correct

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