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: 0.27, 0.15, 0.23, 0.16, and 0.19. Show the probability distribution for the expense forecast. x f(x) 9 10 11 12 13 What is the expected value of the expense forecast for the coming year (to 2 decimals)? What is the variance of the expense forecast for the coming year (to 2 decimals)? If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)?

Answer 1

(a) probability distribution of the expense forecast
x   f(x)

9   0.27

10 0.15

11 0.23

12 0.16

13 0.19

(b)
Expected value E(x) is given by:

x       f                xf                       x² f

9    0.27           2.43                       21.87

10   0.15         1.5                          15

11 0.23           2,53                      27.83

12 0.16          1.92                       23.04

13   0.19         2.47                     32.11

-------------------------------                   -------------

Total               10.85                  119.85

So,

E(x) =

(c)

E(x²) =

Variance = E(x² ) - (E(x))² = 119.85 - 10.85² = 2.1275

(d)
Total expense forecast = 9 + 10 + 11 + 12 + 13 = 55

So,

Expected profit = 55 X 0.16 = 8.80