The mean weight of quarters in circulation must be estimated. How many quarters must we randomly select if we want to be 95% confident that the sample mean is within 0.025 g of the true population mean for all quarters? Based on results from a sample of quarters we can estimate the standard deviation as 0.068 g.

All I really need is the margin of error (e) and I can go from there. But feel free to post the formula so I can be sure. Thanks in advance!

Question

The mean weight of quarters in circulation must be estimated.  How many quarters must we randomly select if we want to be 95% confident that the sample mean is within 0.025 g of the true population mean for all quarters?  Based on results from a sample of quarters we can estimate the standard deviation as 0.068 g.

All I really need is the margin of error (e) and I can go from there. But feel free to post the formula so I can be sure. Thanks in advance!

anonymous · Answer

::sniffle::

kropot72 · Answer

$$\bar{x}+1.96\frac{\sigma}{\sqrt{n}}-(\bar{x}-1.96\frac{\sigma}{\sqrt{n}})=2 \times 0.025$$
$$3.92\frac{\sigma}{\sqrt{n}}=0.05\ ..............(1)$$
Now you can plug the value of sigma into equation (1) and solve for the sample size n.