sample size needed for 95% confidence interval

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BJazz

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An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation of incomes in this region is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. (It’s a pretty poor area being studied.) Given this information, what sample size would the economist need to use if she wanted to develop a 95% confidence interval for average income in the region, with an accuracy (margin of error) of plus/minus $50? (SHOW YOUR WORK IN THE SPACE BELOW.)

I am unsure how to find the desired sample size. Thanks
 
Is this it?

N= Z^2*Omega^2/e^2
Z=1.96
Omega=$1000
E=50
N=(1.96^2)*(1000^2)/(50^2)
=3.8416*1000000/2500
=1536.64
This means that a sample size of 1537 would be needed for a 95% confidence interval of average income in a region.
 
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