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Statistics

Normal Mean Confidence Interval Calculator

Find a mean interval using a supplied critical z value.

Data stays on this deviceConvention explained below

Data and assumptions

Runs on your device

STATISTICAL RESULT

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter sample mean, known population standard deviation, sample size, critical z value.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Margin = z × population SD/√n. Interval = mean ± margin.

A WORKED EXAMPLE

Using sample mean = 50, known population standard deviation = 10, sample size = 100, critical z value = 1.95996398454, the result is 48.04003601546 to 51.95996398454. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

Use the correct critical value and sampling assumptions. This is not a t interval for unknown population variance. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Common questions

Which inputs does this calculation need?

Find a mean interval using a supplied critical z value. Enter sample mean, known population standard deviation, sample size, critical z value. The filled example is editable and is not a saved personal record.

How should I interpret the result?

Use the correct critical value and sampling assumptions. This is not a t interval for unknown population variance. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Methodology maintained by ClarityKit. How these tools are built and checked.