A commonly used IQ test is scaled to have a mean of 100 and a standard deviation 15. A school counselor was curious about the average IQ of the students in her school and took a random sample of fifty students’ IQ scores. The average of these was 107.9. Find a 95% confidence interval for the student IQ in the school.

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= 50Sample 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)