Answer:
The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547
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 the margin of error M as such
In which 
is the standard deviation of the population and n is the size of the sample.
In this question:
So
The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547
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