Question: For large sample size (n), verify that there is a (50-50) chance that the mean of a random sample from an infinite population with the

For large sample size $n$, verify that there is a $50-50$ chance that the mean of a random sample from an infinite population with the standard deviation $\sigma$ will differ from $\mu$ by less than $0.6745 \cdot \sigma / \sqrt{n}$. It has been the custom to refer to this quantity as the probable error of the mean.

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