Historical data indicate that a student’s income for any month of school from work, parents, scholarships, and loans is consistent with the following probability distribution: Income Probability
$750 0.20
$950 0.36
$1150 0.30
$1350 0.14
Expenses for the same student are believed to be consistent with the following probability distribution:
Expense Probability
$900 0.40
$1000 0.25
$1100 0.20
$1200 0.15
Assuming the student begins the school year with a balance of $1200, use Excel to simulate 12 months of activity and to predict the position of the student at the end of the year.

The position of the student at the end of 12 months is $1900

Step-by-step explanation:

From the given information:

The objective of this question is to use Excel to simulate 12 months of activity and to predict the position of the student at the end of the year.

The table below shows the data computed into the excel worksheet and the result gotten.

                                                                                  Initial Balance       1200

Month   U                           Income            Expense   Balance at  month end

1             0.738100256         1150             1100                 1250

2             0.219674065        950             900                  1300

3             0.622637417        1150             1000                 1450

4             0.721004276       1150             1100                   1500

5             0.543855233      950              1000                 1450

6             0.209865042      950              900                  1500

7             0.758422397      1150              1100                   1550

8             0.932588776      1350             1200                  1700

9             0.361888069        950             900                   1750

10             0.343300893      950             900                   1800

11             0.946833427       1350            1200                  1950

12             0.427857569       950             1000                 1900

The position of the student at the end of 12 months is $1900

At U column, a random number is generated from U(0,1)

To generate from the income distribution,  we have:

750 if U<0.2

950 if 0.2<U<0.56

1150 if 0.56<U<0.86

1350 if 0.86<U<1

To generate from the expense distribution, we have:

900 if U<0.4

1000 if 0.4<U<0.65

1100 if 0.64<U<0.85

1200 if 0.85<U<1.00