The student wants to spend a mean of X[bar]=$40 a month for 5 months.
She already spent $35, $65, $20, $70 in 4 months, and you need to calculate how much she has to spend in the 5th month to reach her goal.
The mean can be calculated as
[tex]X\lbrack bar\rbrack=\frac{\Sigma x_i}{n}[/tex]
Where
Σxi is the sum of all observations, in this example, her monthly spending
n is the sample size, in this example the number of months
The information we have is then:
If X[bar] =$40, you can calculate the expenses for the fifth month as follows:
[tex]\begin{gathered} X\lbrack bar\rbrack=\frac{x_1+x_2+x_3+x_4+x_5}{n} \\ 40=\frac{35+65+20+70+x}{5} \\ 40=\frac{190+x}{5} \end{gathered}[/tex]
Multiply both sides by 5
[tex]\begin{gathered} 5\cdot40=5(\frac{190+x}{5}) \\ 200=190+x \\ x=200-190 \\ x=10 \end{gathered}[/tex]
She can spend $10 in December.
