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: 0.29, 0.17, 0.25, 0.07, and 0.22.

1. Show the probability distribution for the expense forecast.
   

   x	f(x)
   9
   10
   11
   12
   13

   
   
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) The probability of expense being $9 millions is 0.29, $10 is 0.17, $11 is 0.25, $12 is 0.07 and $13 is 0.22.

Hence the  probability distribution for the expense forecast is

x	f(x)
9	0.29
10	0.17
11	0.25
12	0.07
13	0.22

b) the expected value of X is

ans: the expected value of the expense forecast for the coming year is $10.76 millions

c) The variance of X is calculated as

First the expectation of

Now the variance is

ans: the variance of the expense forecast for the coming year is 2.22

c) The profit is

where Expense is the variable X in part a)

The expected value of Profit is

ans: If income projections for the year are estimated at $12 million, the college expect to make a profit of $1.24 millions