When to use this calculator
Find a symmetric normal-model interval from a mean, known population deviation and chosen critical value. Requires a suitable normal-model mean interval with known population deviation. Unknown-deviation small samples need a t-based method.
Explore the sampling uncertainty calculators for other questions in this topic. For a related calculation, use the Proportion Standard Error Calculator: Estimate the standard error of a sample proportion under a simple independent-sampling model.
PUTTING IT INTO PRACTICE
Normal Mean Confidence Interval: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Sample mean | 50 |
| Known population standard deviation | 10 |
| Independent sample size (integer) | 100 |
| Chosen z critical value | 1.96 |
| Result | 48.04 to 51.96 input measurement units |
- Check the input labels and enter the example values above.
- Apply the relationship: Interval = mean ± z × known population standard deviation/√n..
- The result is 48.04 to 51.96 input measurement units, rounded for display.
How to interpret your result
Requires a suitable normal-model mean interval with known population deviation. Unknown-deviation small samples need a t-based method.
Use a critical value and model appropriate to the study. Simple random-sampling approximations do not correct for selection bias or clustered observations. Normal approximations can be poor for small samples or extreme proportions.
Frequently asked questions
Does a larger sample remove selection bias?
No. More observations can reduce sampling variability without repairing a systematically biased selection process.
When is the normal mean confidence interval calculator useful?
Find a symmetric normal-model interval from a mean, known population deviation and chosen critical value. Requires a suitable normal-model mean interval with known population deviation. Unknown-deviation small samples need a t-based method.
How do I use the normal mean confidence interval calculator?
Enter sample mean, known population standard deviation, independent sample size (integer), chosen z critical value. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Interval = mean ± z × known population standard deviation/√n..
What should I check before using the result?
Requires a suitable normal-model mean interval with known population deviation. Unknown-deviation small samples need a t-based method.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST/SEMATECH statistical methods handbook ↗. This is a topic reference, not an external review or endorsement of this tool.
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