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A quality control engineer would like to estimate the mean fill amount of a certain bottle-filling machine to within 0.05 liter. If we assume that the population standard deviation is 0.17 liters, how large of a sample is needed to estimate mu with 95% confidence?

A random sample of 35 trading days is taken and the volume of a particular stock is recorded to determine whether the mean volume of the stock has changed from its 2007 value of 35.14 million shares. The sample resulted in a mean trading volume of > = 39.48. Assuming a population standard deviation of 15.07, compute the margin of error for a 95% confidence interval for mu.

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