Statistics
Mean confidence interval, known SD Calculator
Calculate a two-sided normal confidence interval when population SD is known. This free mean confidence interval, known sd calculator shows the calculation and its assumptions so you can compare your own figures.
Your results
Calculate a two-sided normal confidence interval when population SD is known.
Calculated outcomes
- Margin Of Error
- 2.9399
- Standard Error
- 1.5
Assumptions and estimates
- Two-sided normal z interval with known population standard deviation, independent observations and a normally distributed mean. An estimated sample standard deviation requires a t interval; this calculator does not substitute z for t. A confidence interval is not a prediction interval for an individual observation.
- Method: Mean ± z × known population SD / √n. Use a t method if SD is estimated from the sample.
- Editable inputs are planning assumptions; check the method and result notes for scope.
Useful next steps
- Use Compare options to test an alternative side by side.
- Copy, print or download a record of this calculation when you need one.
Reports open your email app addressed to s@s1.ie with the public page address only. Your inputs are never added.
How the mean confidence interval, known sd calculation works
Mean ± z × known population SD / √n. Use a t method if SD is estimated from the sample.
Editable inputs are planning assumptions; check the method and result notes for scope.
Using this calculator
- Enter your own figures in the labelled inputs. Keep the currencies, units and time periods consistent.
- Choose any applicable rate profile, pattern or assumption shown for this tool. Open additional inputs when relevant.
- Review lower confidence bound and upper confidence bound, then read the stated assumptions and eligibility conditions before using the result.
Worked example
This is a static example using illustrative inputs, not facts about you or today’s date. The displayed eligibility selections and assumptions apply only to this example.
See example inputs
- Observed sample mean
- 100
- Known population standard deviation
- 15
- Independent sample size
- 100
- Confidence level
- 95%
- Lower Confidence Bound
- 97.0601
- Upper Confidence Bound
- 102.9399