Confidence Interval Calculator

Find a confidence interval for a mean.

Sample mean

Standard deviation

Sample size

Confidence level

Lower bound 95.1

Upper bound 104.9

Margin of error 4.9

Formula: CI = mean ± z × σ ÷ √n

Step-by-step with your numbers:

1. Values used:

2. Sample mean = 100

3. Standard deviation = 15

4. Sample size = 36

5. Confidence level = 1.96

7. Lower bound = 95.1

8. Upper bound = 104.9

9. Margin of error = 4.9

Did we solve your problem today?

A confidence interval is a range likely to contain the true mean.

The math behind it

CI = sample mean ± z × (σ ÷ √n). z is 1.645 (90%), 1.96 (95%), 2.576 (99%).

mean 100, σ 15, n 36, 95% → 95.1 to 104.9.

Small samples?

Use the t-distribution instead of z for small n.