Answer: (103.74,112.06)
Step-by-step explanation:
The confidence interval for population mean is given by :_
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Given : Sample size : n= 50
Sample mean : [tex]\overline{x}=107.9[/tex]
Standard deviation : [tex]\sigma=15[/tex]
Significance level : [tex]\alpha: 1-0.95=0.5[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Then the 95% confidence interval for the student IQ in the school will be :-
[tex]107.9\pm (1.96)\dfrac{15}{\sqrt{50}}\\\\\approx107.9\pm0.075\\\\=(107.9-4.16,107.9+4.16)=(103.74,112.06)[/tex]
Hence, the 95% confidence interval for the student IQ in the school= (103.74,112.06)
