Answer: [tex](587.67,596.33)[/tex]
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 mean : [tex]\overline{x}= 592 [/tex] hours
Standard deviation[tex]\sigma= 25[/tex] hours
Sample size : n=90, which is a large sample(n<30), so we use z-test.
Significance level: [tex]1-0.90=0.1[/tex]
Critical value : [tex]z_{\alpha/2}=t_{22,0.025}=1.645[/tex]
Then , the confidence interval for population mean will be :-
[tex]592\ \pm\ (1.645)\dfrac{25}{\sqrt{90}}\\\\\approx592\pm4.33\\\\=(592-4.33,592+4.33)\\\\=(587.67,596.33)[/tex]
Hence, the 90% confidence interval for the mean life [tex]\mu[/tex] of all light bulbs of this type. is [tex](587.67,596.33)[/tex]
