Answer: (47.51, 54.49)
Step-by-step explanation:
Confidence interval for population mean is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
, where n= sample size .
[tex]\sigma[/tex] = population standard deviation.
[tex]\overline{x}[/tex] = sample mean
[tex]z_{\alpha/2}[/tex] = Two -tailed z-value for [tex]{\alpha[/tex] (significance level)
As per given , we have
[tex]\sigma=11.8\text{ ounces}[/tex]
[tex]\overline{x}=51 \text{ ounces}[/tex]
n= 44
Significance level for 95% confidence = [tex]\alpha=1-0.95=0.05[/tex]
Using z-value table ,
Two-tailed Critical z-value : [tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]
Now, the 95% confidence interval for the true population mean textbook weight will be :-
[tex]51\pm (1.96)\dfrac{11.8}{\sqrt{44}}\\\\=51\pm(1.96)(1.7789)\\\\=51\pm3.486644\approx51\pm3.49\\\\=(51-3.49,\ 51+3.49)\\\\=(47.51,\ 54.49) [/tex]
Hence, the 95% confidence interval for the true population mean textbook weight. : (47.51, 54.49)
