Confidence Interval Calculator
Compute the confidence interval for a sample mean — enter the mean, standard deviation, and sample size to get the lower and upper bounds.
Lower bound
94.63
Breakdown
- Upper bound
- 105.37
- Margin of error (±)
- 5.37
- Standard error
- 2.74
Last updated:
FAQ
What does a 95% confidence interval mean?
If you repeated the sampling many times, about 95% of the intervals built this way would contain the true population mean. It is a statement about the method's long-run reliability, not a 95% probability for one specific interval.
When can I use this z-based formula?
When the sample is reasonably large (n ≥ 30) or the population standard deviation is known. For small samples from a normal population, a t-distribution interval is slightly wider — this calculator approximates with z.
Why does a bigger sample narrow the interval?
The margin shrinks with the square root of n: quadrupling the sample halves the interval width. That square root is why precision gets progressively more expensive to buy.
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