Ans. Option ii
The probability distribution table for total profit is,
Q = Quantity and Pq is its probability
g = profit per unit and Pg is its probability
G = total profit = Q*G and P = probability = Pq*Pg
Q. Pq. g. Pg. G. P
100 0.4 5 0.35 500 0.14
100 0.4 7 0.65 700 0.26
125 0.6 5 0.35 625 0.21
125. 0.6. 7. 0.65. 875. 0.39
E(G) = Expected value of total Gain = Sum of (P*G)
=> E(G) = 500*0.14 + 700*0.26 + 625*0.21 + 875*0.39
=> E(G) = 70 + 182 + 131.25 + 341.25 = $724.5
For standard deviation,
E(G^2) = Sum of (P*G^2) = 35000 + 127400 + 82031.25 + 298593.75
=> E(G^2) = 543025
Standard deviation = (E(G^2) - (E(G))^2)^0.5
=> Standard deviation = (543025 - 524900.25)^0.5
=> Standard deviation = 134.628
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