Hooper Chemical Company, a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process, is examining a plastics firm to add to its operations. Before the acquisition, the normal expected outcomes for the firm were as follows: Outcomes ($ millions) Probability Recession $ 10 0.3 Normal economy 50 0.5 Strong economy 60 0.2 Compute the expected value, standard deviation, and coefficient of variation prior to the acquisition. (Do not round intermediate calculations. Enter your dollar answers in millions rounded to 2 decimal places (e. g., $12,300,000 should be entered as "12.30"). Round the coefficient of variation to 3 decimal places.)

Question

Business

Ricardo Hansen

28 May, 12:25

Hooper Chemical Company, a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process, is examining a plastics firm to add to its operations. Before the acquisition, the normal expected outcomes for the firm were as follows: Outcomes ($ millions) Probability Recession $ 10 0.3 Normal economy 50 0.5 Strong economy 60 0.2 Compute the expected value, standard deviation, and coefficient of variation prior to the acquisition. (Do not round intermediate calculations. Enter your dollar answers in millions rounded to 2 decimal places (e. g., $12,300,000 should be entered as "12.30"). Round the coefficient of variation to 3 decimal places.)

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Answers (1)

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Skyler Andrade · Answer 1

Expected Value (EV) = 40

Standard Deviation = 20

Coefficient of Variation = 0.5

Explanation:

Outcomes ($ millions) Probability

Recession $10 0.3

Normal Economy $50 0.5

Strong economy $60 0.2

Expected value, μ = Outcome * probability

= ($10 * 0.3) + ($50 * 0.5) + ($60 * 0.2) = 3 + 25 + 12 = 40

∑ (x₁ - μ) ²

Standard deviation, σ = √ (∑ (x₁ - μ) ²) / N

X = Outcomes

μ = Expected value

X (x - μ) (x₁ - μ) ² (x₁ - μ) ²) * Probability

10 10 - 40 = - 30 900 900 * 0.3 = 270

50 50 - 40 = 10 100 100 * 0.5 = 50

60 60 - 40 = 20 400 400 * 0.2 = 80

Total = 400

Standard deviation = √400 = 20

Coefficient of Variation = Standard deviation / Mean

= 20 / 40

= 0.5