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Statistics Math Problem

In a standardized test for lawyers, scores are normally distributed and the standard deviation is known to be 28.5 points. How large of a sample must to find the estimate the mean score of all lawyers taking this test if you want the margin of error to be less than 10 points. Use a 95% level of confidence
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1 Answer

To find the required sample size for the mean score, we can use the formula:
 
n = (zc sigma / E)^2
 
where
n is the sample size
zc is the critical value associated with 95% confidence, in this example zc = 1.96
sigma is standard deviation
E is margin of error.
 
Thus we have:
n = (zc sigma / E)^2
n = (1.96 * 28.5 / 10)^2
n = 31.2
 
We always round samples sizes in these questions up to the next higher number so the sample size here would be 32