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Consider a researcher would like to see how large a sample is needed to estimate the average monthly income. Assume that monthly income is normally

Consider a researcher would like to see how large a sample is needed to estimate the average monthly income. Assume that monthly income is normally distributed. The population standard deviation is believed to be 4000. The research would like to estimate a 95% confidence interval for the sample mean.

(a) How large a sample is needed if the margin of error is 1000?

(b) How large a sample is needed if the margin of error is 250?

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