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: 0.3, 0.17, 0.24, 0.08, and 0.21.

1. Show the probability distribution for the expense forecast (to 2 decimals).
   

   x	f(x)
   9	.30
   10
   11	.25
   12
   13	.20

   
   
2. What is the expected value of the expense forecast for the coming year (to 2 decimals)?
     
   
3. What is the variance of the expense forecast for the coming year (to 2 decimals)?
     
   
4. 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

b. Expected Value

c. Variance

d. Profit = Income - Expected Costs

Profit = $12 Million - $10.73 Million

Profit = $1.27 Million

The College is in a good financial position as there is profit.