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 | $ | 20 | 0.2 | |||
Normal economy | 40 | 0.4 | ||||
Strong economy | 50 | 0.4 | ||||
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.)
Expected value = sum of ( probability * outcome)
Standard deviation = sum of [ probability * ( outcome - expected value )^2 ] ^0.5
State of economy | Probability ( P) | Outcome (x) | Px | (x - sum of Px | (x-sum of Px)^2 | P*(x-sum of Px)^2 |
Recession | 0.2 | 20 | 4 | -20 | 400 | 80 |
Normal Economy | 0.4 | 40 | 16 | 0 | 0 | 0 |
Strong Economy | 0.4 | 50 | 20 | 10 | 100 | 40 |
Expected Value | 40 | VARIANCE | 120 |
Expected value = 40 million dollars
Standard deviation = 120^0.5 = 10.95 million
coefficient of variation = standard deviation / mean = 10.95 / 40 = 0.274
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