How it works
Interval = sample mean ± z×known population sigma/sqrt(sample size).
Input definitions
- Sample mean
- Enter the value in the labeled unit.
- KNOWN population standard deviation
- Enter the value in the labeled unit.
- Sample size
- Enter the value in the labeled unit.
- Two-sided confidence
- Choose 90% / 95% / 99%.
A worked example
- Sample mean
- 100
- KNOWN population standard deviation
- 15
- Sample size
- 100
- Two-sided confidence
- 95%
Assumptions & limits
Known population sigma only; not a Student t interval using sample SD. Does not establish random sampling, normality or coverage for small non-normal samples.
Sources & review
Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.
Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.
Common questions
Why can statistical results differ between tools?
Denominator, interpolation and boundary conventions can differ. Use the method and assumptions on this page to compare the same definition; displayed decimals may also be rounded.
How does the Mean confidence interval — known sigma tool work?
Interval = sample mean ± z×known population sigma/sqrt(sample size).
What are the assumptions and limits of Mean confidence interval — known sigma?
Known population sigma only; not a Student t interval using sample SD. Does not establish random sampling, normality or coverage for small non-normal samples.