Step 1
Given;
[tex]\begin{gathered} n=381\text{ adults} \\ Mean\text{ \lparen}\mu)=65.2 \\ \sigma=2.8 \end{gathered}[/tex]
Step 2
The confidence interval is given as follows;
[tex]CI=\mu\pm t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n}})[/tex]
The test statistic for a 95% confidence interval with α = 0.05, the degrees of freedom, df= n-1 = 381-1=380
[tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.05}{2},380}[/tex][tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.05}{2},380}=1.97[/tex][tex]\begin{gathered} C.I=65.2\pm1.97(\frac{2.8}{\sqrt{381}})=65.2\pm0.2825932406 \\ C.I=(64.92,65.48) \end{gathered}[/tex]
Answer;
[tex]C.I=(64.92,65.48)[/tex]
