Answer: [tex](57.41,\ 62.19)[/tex]
Step-by-step explanation:
Given : Sample size : [tex]n=40[/tex]
Sample mean : [tex]\overline{x}=59.8\text{ seconds}[/tex]
Standard deviation : [tex]\sigma =9.2\text{ seconds}[/tex]
Significance level : [tex]\alpha=1-0.9=0.1[/tex]
Critical value : [tex]z_{\alpha/2}=1.645[/tex]
Formula to find the confidence interval for population mean :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=59.8\pm(1.645)\dfrac{9.2}{\sqrt{40}}\\\\\approx59.8\pm2.39\\\\=(59.8-2.39,\ 59.8+2.39)\\\\=(57.41,\ 62.19)[/tex]
Hence, a 90% confidence interval estimate of the population mean of all students = [tex](57.41,\ 62.19)[/tex]
