Question

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.)
  

Answer 1

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