Answer:
i)
So then the 90% confidence interval is given by (1.959, 2.041)
ii) Figure attached
iii)
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The confidence interval is given by this formula:
(1)
And for a 90% of confidence the significance is given by , and
. Since we know the population standard deviation we can calculate the critical value
We know the folllowing data:
represent the sample mean
represent the population deviation
n =16 represent the sample size
Part i)
If we replace the values given into formula (1) we got:
So then the 90% confidence interval is given by (1.959, 2.041)
Part ii)
Figure attached. We have the illustration for the confidence interval obtained.
Part iii)
The margin of error is given by:
And if we replace we got:
