Question

The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.2, 0.3, 0.2, 0.05, and 0.25. (a) Show the probability distribution for the expense forecast. x f(x) 9 10 11 12 13 (b) What is the expected value (in $ millions) of the expense forecast for the coming year? $ million (c) What is the variance of the expense forecast for the coming year? (d) If income projections for the year are estimated at $12 million, comment on the financial position of the college. With this estimate, the college can expect a profit (in $ million) of $ million. From the assigned probability, there is chance that expenses will equal $13 million causing the college to run a

Answer 1

a)

x	P(x)
9	0.2
10	0.3
11	0.2
12	0.05
13	0.25

b)

x	P(x)	xP(x)	x2P(x)
9	0.2	1.800	16.200
10	0.3	3.000	30.000
11	0.2	2.200	24.200
12	0.05	0.600	7.200
13	0.25	3.250	42.250
	total	10.850	119.850
	E(x) =μ=	ΣxP(x) =	10.8500
	E(x2) =	Σx2P(x) =	119.8500
	Var(x)=σ2 =	E(x2)-(E(x))2=	2.1275

expected value =10.85

c)variance of the expense forecast =2.1275

d)

If income projections for the year are estimated at $12 million, comment on the financial position of the college. With this estimate, the college can expect a profit $1.15 million
From the assigned probability, there is chance that expenses will equal $13 million causing the college to run a loss