Answer: (129.04,130.96)
Step-by-step explanation:
Given : Sample size : n= 145
Mean IQ in the sample : [tex]\overline{x}=130[/tex]
Standard deviation : [tex]\sigma=7[/tex]
Significance level : [tex]\alpha=1-0.9=0.1[/tex]
Critical value : [tex]z_{\alpha/2}=1.645[/tex]
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=130\pm(1.645)\dfrac{7}{\sqrt{145}}\\\\=130\pm0.96\\\\=(129.04,\ 130.96)[/tex]
Hence, the 90% confidence interval for the students' mean IQ score is (129.04,130.96)
