Margin of Error Calculator

The calculator will find the margin of error from the given sample size and distribution, with steps shown.

Sample size: n=

Confidence level: %

standard deviation:

Distribution used:
If the population standard deviation is known or the sample size is n>30, normal distribution will be chosen automatically. To force another distribution, choose it explicitly.

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Solution

Your input: find the margin of error for the sample size $$n=64$$$, standard deviation $$\sigma=7$$$, and confidence level $$95.0 \%$$$using normal distribution. First, find the critical value: $$z_{\frac{\alpha}{2}}=1.95996398454005$$$

Next, find the standard error of the mean: $$SE=\frac{\sigma}{\sqrt{n}}=\frac{7}{8}$$$Finally, the margin of error is $$ME=z_{\frac{\alpha}{2}} \cdot SE=1.95996398454005 \cdot \left(\frac{7}{8}\right) \approx 1.71496848647255$$$

Answer: $$ME=1.71496848647255$$\$