Answer:
The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find M as such
In which is the standard deviation of the population and n is the size of the sample.
The standard deviation is the square root of the variance. So
Then
The lower end of the interval is the mean subtracted by M. So it is 1.75 - 0.0392 = 1.7108m
The upper end of the interval is the mean added to M. So it is 1.75 + 0.0392 = 1.7892m
The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.