Given that the Confidence Interval for a population mean:
[tex]11.81<\mu<13.21[/tex]
In this case, you can set up these two equations:
[tex]\bar{x}+E=13.21\text{ \lparen Equation 1\rparen}[/tex]
[tex]\bar{x}-E=11.81\text{ \lparen Equation 2\rparen}[/tex]
Because by definition:
[tex]\bar{x}-E<\mu<\bar{x}+E[/tex]
Where "ME" is the margin of error and this is the mean:
[tex]\bar{x}[/tex]
In this case, in order to find the "ME", you need to follow these steps:
1. Add Equation 1 and Equation 2:
[tex]\begin{gathered} \bar{x}+E=13.21 \\ \bar{x}-E=11.81 \\ -------- \\ 2\bar{x}=25.02 \end{gathered}[/tex]
2. Solve for the mean:
[tex]\begin{gathered} \bar{x}=\frac{25.02}{2} \\ \\ \bar{x}=12.51 \end{gathered}[/tex]
3. Substitute the mean into Equation 1 and solve for "ME":
[tex]12.51+E=13.21[/tex][tex]\begin{gathered} E=13.21-12.51 \\ E=0.7 \end{gathered}[/tex]
Hence, the answer is:
[tex]E=0.7[/tex]
