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How to find the sample size to estimate population mean.

A company is attentive in estimating μ the mean number of days of sick leave taken by its employees. The firm's statistician randomly selects 100 personnel files and notes the number of sick days taken by each employee. The sample mean is 12.2 days as well as the sample standard deviation is 10 days. How many personnel files would the director have to select in order to estimate m to within 2 days with a 99% confidence interval?

A. 2
B. 13
C. 136
D. 165
E. 166

Statistics and Probability, Statistics

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