Answer:
The 95% confidence interval is (135.0285 degrees, 189.9715 degrees).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find M as such
[tex]M = z*s[/tex]
In which s is the standard deviation of the sample. So
[tex]M = 1.645*16.7 = 27.4715[/tex]
The lower end of the interval is the mean subtracted by M. So it is 162.5 - 27.4715 = 135.0285 degrees
The upper end of the interval is the mean added to M. So it is 162.5 + 27.4715 = 189.9715 degrees
The 95% confidence interval is (135.0285 degrees, 189.9715 degrees).
