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Answer:
The 95% confidence interval for the population mean is between 61.5 and 68.5.
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 lower end of the interval is the sample mean subtracted by M. So it is 65 - 3.5 = 61.5
The upper end of the interval is the sample mean added to M. So it is 65 + 3.5 = 68.5
The 95% confidence interval for the population mean is between 61.5 and 68.5.