how large a random sample is needed

Statistics
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consider a population having a standard deviation equal to 5.0 we wish to estimate the mean of this population. how large a random sample is needed to construct a 99 percentile confidence interval for the mean of this population with a margin of error equal to .2?

May 12th, 2015

We want the max deviation of estimate from the mean: |X-mu| = 0.2

We want the confidence interval to be 1% or 0.5% from either side of the bell curve

From the normal distribution table we find that for this we must have: |X-mu|/(sigma/sqrt(n))<2.57

thus: (sigma/sqrt(n))<0.2/2.57

we have sigma =5 so sqrt (n) > 5*2.57/0.2 => n> (5*2.57/0.2)^2=4128

May 12th, 2015

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May 12th, 2015
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May 12th, 2015
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