Answer:
The lower bound of the interval is 88.9mm and the upper bound is 93.1mm.
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{1-0.85}{2} = 0.075[/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]1-0.075 = 0.925[/tex], so [tex]z = 1.44[/tex]
Now, find M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.44*\frac{8}{\sqrt{30}} = 2.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 91 - 2.1 = 88.9mm.
The upper end of the interval is the sample mean added to M. So it is 91 + 2.1 = 93.1 mm
The lower bound of the interval is 88.9mm and the upper bound is 93.1mm.
