Answer:
(48.3875, 51.6125)
Step-by-step explanation:
At 99% level of significance
[tex]\alpha=1-0.99=0.01[/tex]
[tex]Z_{a\lpha /2}=0.01/2=0.005[/tex]
From the normal standard deviation table [tex]Z_{a\lpha /2}=2.33[/tex]
Considering that
[tex]\bar x[/tex] ± [tex]Z_{a\lpha /2} \frac {\sigma}{\sqrt{n}}[/tex]=50±[tex]2.33\frac {5}{\sqrt {64}}[/tex]
50±2.33(0.625)=50±1.6125=(48.3875, 51.6125)
Therefore, there’s 99% confidence that the mean lifetime of a certain brand of tires is between 48.3875 and 51.6125
