Given that:
- You measure 50 textbooks' weights.
- They have a Mean of 77 ounces.
- The Population Standard Deviation is 12.3 ounces.
You need to use the following formula:
[tex]CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}[/tex]Where:
- The Sample Mean is:
[tex]\bar{x}[/tex]- The z-value for the corresponding Confidence Interval Level is "z".
- The Sample Standard Deviation is σ.
- The Sample Size is "n".
In this case:
[tex]\begin{gathered} \bar{x}=77 \\ \sigma=12.3 \\ n=50 \end{gathered}[/tex]By definition, for a 95% Confidence Interval:
[tex]z=1.96[/tex]Then, by substituting values and evaluating, you get these two values:
[tex]CI=77+1.96\cdot\frac{12.3}{\sqrt{50}}\approx80.41[/tex][tex]CI=77-1.96\cdot\frac{12.3}{\sqrt{50}}\approx73.59[/tex]Hence, the answer is:
[tex]73.59<\mu<80.41[/tex]