32E

Answer : Step 1 : Given certain of upright freezer is available in three different rated capacities : 3 3 3 16 ft , 168ft , 20 ft Let x = the rated capacity of freezer of this brand sold at a certain store. Suppose that pmf x p(x) 16 0.2 18 0.5 20 0.3 2 a). Now we have to compute E(X),E(X ) and V (X) So E(X) = 16 × 0.2 + 18 × 0.5 + 20 × 0.3 E(X) = 3.2 + 9 + 6 E(X)= 18.2 Then, 2 2 2 2 E(X ) = 16 × 0.2 + 18 × 0.5 + 20 × 0.3 E(X ) = 256 × 0.2 + 324 × 0.5 + 400 × 0.3 E(X ) = 51.2 + 162 + 120 2 E(X ) = 333.2 The formula of the v(x) is 2 2 V (X) = E(X ) (E(X)) 2 V (X) = 333.2 (18.2) V (X) = 333.2 (331.24) V (X) = 1.96 2 Therefore E(X) = 18.2,E(X ) = 333.2 and V (X) = 1.96 Step 2 : b). We know that if the price of a freezer having capacity x is 70x-650. We have h(x) = 70x - 650 So the possible values are x=16,x=18 and x=20 Put x = 16 h(x) = 70x - 650 h(16) = 70(16) - 650 h(16) = 1120 - 650 h(16) = 470 Put x=18 h(x) = 70x - 650 h(16) = 70(18) - 650 h(16) = 1260 - 650 h(16) = 610 Put x=20 h(x) = 70x - 650 h(16) = 70(20) - 650 h(16) = 1400 - 650 h(16) = 750 Now we have to find the expected price paid by the next customer to buy a freezer. We calculate E(h(x)) as E(h(x)) = 470 × 0.2 + 610 × 0.5 + 750 × 0.3 E(h(x)) = 94 + 305 + 225 E(h(x)) = 624 Therefore the expected price paid by the next customer to buy a freezer is 624.