# Margin of Error Calculator

## Calculate margin of error step by step

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.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

### 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: $ME=1.71496848647255$