What is this calculator?
Estimate a normal-approximation confidence interval around a mean.
What can you use it for?
Use it when solving an exercise, checking a result, or working with the particular quantities shown in this form. Estimate a normal-approximation confidence interval around a mean.
How to use it
- Enter sample mean.
- Enter sample standard deviation.
- Enter sample size.
- Enter critical z value.
- Select Calculate (or Generate for random tools).
- Read the answer and any additional results below the form. Check the units and the limits of the method.
Formula and method
Upper bound = sample mean+critical z value × sample standard deviation/sqrt(sample size)
Margin of error = critical z value × sample standard deviation/sqrt(sample size)
The formula uses the units and definitions shown above. Each input is substituted before the arithmetic is evaluated; the calculated output is rounded for display.
Worked example
Sample mean: 50, Sample standard deviation: 10, Sample size: 100, Critical z value: 1.96. The result is 48.04 (lower bound).
Assumptions and limits
Normal z approximation. Small samples may require a t interval. Enter the appropriate critical value.
Frequently asked questions
What inputs does the Confidence Interval Calculator need?
Use sample mean, sample standard deviation, sample size, critical z value. Read the answer and any additional results below the form. Check the units and the limits of the method.
What assumptions apply to the Confidence Interval Calculator?
Normal z approximation. Small samples may require a t interval. Enter the appropriate critical value.