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Sample size for estimating a population mean

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Please help with the following problem.

It is believed that the range of hourly wages paid to auto mechanics in a large city is $9 (range approx. = 4sigma-squared). If we assume that hourly wages are approximately normally distributed, how large a sample is necessary so that with probability 0.99 the sample mean will be within one dollar of the true average hourly wages?

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This solution shows how to determine the sample size necessary to construct a confidence interval for a population mean when the margin of error must be within a given amount and the interval must have a given level of confidence.

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1. It is believed that the range of hourly wages paid to auto mechanics in a large city is $9 (range approx. = 4sigma-squared). If we assume that hourly wages are approximately normally distributed, how large a sample is necessary so that with probability 0.99 the sample mean will be within one dollar of the true average hourly wages?

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