The normal-approximation interval is approximately 69.65 to 74.35.
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Confidence Interval Calculator
Enter the sample mean, standard deviation, sample size and confidence level to estimate the interval and margin of error.
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Confidence interval details
Formula & disclaimer
Confidence Interval = Sample Mean Β± Critical Z Γ (Sample Standard Deviation Γ· βSample Size)
View assumptionsFormula reviewCalcs at Hand Editorial TeamVerified 31 August 2026 Β· automated checks included
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Three useful checks, kept deliberately short.
Mean 72, standard deviation 12, sample size 100 and 95% confidence: Calculate the standard error Β· Multiply by 1.96 Β· Add and subtract the margin.
This version uses a normal critical value and is most suitable for large samples or known population variability.
Formula and assumptions
Confidence Interval = Sample Mean Β± Critical Z Γ (Sample Standard Deviation Γ· βSample Size)A wider confidence level produces a wider interval when the sample stays unchanged.
Keep in mind: Check sampling design, independence, distribution assumptions and whether a t-based method is more appropriate.
Produced byCalcs at Hand Editorial Team
Last formula check31 August 2026
Review methodKnown examples + boundary cases
Editorial and correction policy β