# Confidence Interval Using Normal Distribution Calculator

  

An online and easy to use calculator that calculates the confidence interval with a certain percentage, using the normal distribution , is presented.
An online confidence interval using t distribution calculator is included.

## Definition of Confidence Interval for the Normal Distribution

For a sample of size $n$ from a population that has a standard deviation $\sigma$, we define a $(1-\alpha)100\%$ confidence interval for $\mu$ as $\bar X \pm Z_{\alpha/2} \dfrac{\sigma}{\sqrt n}$ We say that we are $(1-\alpha)100\%$ confident that the mean $\mu$ of the population is within the interval $\left[\bar X - Z_{\alpha/2} \dfrac{\sigma}{\sqrt n} \quad , \quad \bar X + Z_{\alpha/2} \dfrac{\sigma}{\sqrt n} \right]$.
The graphical meaning of an interval of confidence is shown below.

Note that: $\quad \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 1$
The above definition is used when the standard deviation $\sigma$ of the population $P$ is known and
1) either the population $P$ is normally distributed
2) or the population $P$ is NOT normally distributed but the sample size $n$ is greater than $30$.

## Confidence Interval Calculator

Enter the sample size $n \ge 30$ as a positive integer, the sample mean $\bar X$, the population standard deviation $\sigma$ as a positive real number and the level of confidence (percentage) as a positive real number greater than $0$ and smaller than $100$.

Sample Size: $n$ =       Sample Mean: $\bar X$ =       Population Standard Deviation: $\sigma$ =       Confidence Level = $\%$
Decimal Places =