Confidence interval · known population deviation
Confidence interval · known population deviation: use sample mean, known population standard deviation, sample size. Review the formula, worked example and calculation steps.
Inputs
Use the units shownEnter your values and select Calculate.
Formula & explanation
Variables & units
- Sample mean
- Numeric value · minimum -1000000000000, maximum 1000000000000
- Known population standard deviation
- Numeric value · minimum 0.000001, maximum 1000000000000
- Sample size
- Numeric value · minimum 1, maximum 1000000000
- Confidence level
- Select an option
Worked example
Mean 100, known σ=15, n=100 and 95% confidence gives approximately 97.060054 to 102.939946.
Assumptions
Requires independent observations and normal sampling distribution (or an appropriate large-sample approximation). Known population σ only; use a t interval when estimating σ from a small sample.
References
Formula version 1.0.0. JavaScript floating-point arithmetic applies. Results display up to 6 decimal places; stored values retain available precision. Use the units shown.
Practice with an example
Use the default input values to find the answer. The reset icon restores those values.
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