Answer: [tex](103.3515,\ 112.6485)[/tex]
Step-by-step explanation:
According to the given information, we have
n= 40
[tex]\sigma=15\\\\\overline{x}=108[/tex]
Critical z-value for 95% confidence = [tex]z_{\alpha/2}=1.96[/tex]
Confidence interval :
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=108\pm (1.96)\dfrac{15}{\sqrt{40}}\\\\\approx108\pm4.6485\\\\= (108-4.6485,\ 108+4.6485)\\\\=(103.3515,\ 112.6485)[/tex]
Hence, the 95 percent confidence interval for this result : [tex](103.3515,\ 112.6485)[/tex]
