Confidence Interval Calculator – Known Population SD: 90-percent
Estimate a population mean with known standard deviation.
Formula
CI = mean ± zσ/√n; z ≈ 1.645, 1.960, 2.576.
Margin of error ≈ 1.645×(10)÷sqrt((100)) · Lower bound ≈ (50)-(1.645) · Upper bound ≈ (50)+(1.645)
How to use
- Enter the sample mean and known population SD.
- Enter sample size and choose confidence.
- Read both bounds and the margin of error.
Examples
- Mean 50, σ 10, n 100: 95% CI ≈ [48.04, 51.96].
Frequently asked questions
When is this valid?
Use an independent random sample from a normal population, or a sufficiently large sample for the normal approximation.
Can I enter the sample SD?
This model requires known population σ. If σ is estimated, a Student t interval is generally needed.
What does 95% mean?
About 95% of intervals from repeated samples cover the fixed population mean. Critical values here are rounded.
Sources
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