Question

Answer the following multiple-choice question. You have to select the correct option and provide a complete correct solution.

e. The production rate of a company (D) could be 100 units per year with a probability of 0.4 or 125 units per year with a probability of 0.6. Moreover, the profit per unit sold (S) is either $5 with a probability of 0.35 or $7 with a probability of 0.65. What are the expected value and the standard deviation of the total annual profit (P)? i. 724.5 and 132 ii. 724.5 and 134.6 iii. 832.5 and 98.7 iv. 924.8 and 110.5

Answer 1

5 5 1 Quantity X Profit peruni 100 X 5 = 500 Probability o.uxo.35 2. 35 100 16.4 S 7 0.65 too X •Proby 700 0.4 0.65 0,35) 5 125 X 5 : 1625 • Proby 0. 620.35 06 S 125 125 x 7 875 • probe -0.600.65 0.65 7 Probability Total Profit (P) 500 700 625 875 (*) 0.14 0,26 0.21 0.39

Diese prx P2 P x P.X 0.14 0.26 625 0.21 875 0.39 182 131.25 341. 25 (Ep.x 724,5 2 50000 499000 390,625 765,625 px 35,000 127400 82031.25 298593.75 543,025 Expected value of Total annual profit (1) EP.X $724.5 Standard deviation of P square of Variance off reot V Varle Vie)E(P2) - (ECP)] E(P²) EP²x 54 3025 724.5 . ELP) - Vo = 543025 (724.57 181 24.75 Standard Deviation. = 8 124.75 $ 134.6 JVP
The right answer is option ii) 724.5 and 134.6

To calculate the total annual profit,

P= Total units × profit per unit

To calculate the probabilities of total annual profits;

X= Probability of the profit × probability of the number of units

Formulas for expectation and standard deviation is attached. Please refer to that for all the calculation part.