Standard Normal Distribution Calculator

Enter the normal random variable (X), mean (μ), and stand deviation (σ) into the standard normal distribution calculator. The calculator will return the standard normal distribution, also known as the z-score.

Standard Normal Distribution Formula

The following formula is used to calculate the standard normal distribution:

z = (X – μ) / σ

• Where Z is the standard normal distribution
• X is the normal random variable
• μ is the mean
• σ is the standard deviation

How to calculate the standard normal distribution

1. First, determine the normal random variable

Using the information provided or the formula Y = { 1/[ σ * sqrt(2π) ] } * e-(x – μ)2/2σ2 , determine the normal random variable.

2. Determine the average

Calculate the mean or average of the data set

3. Determine the standard deviation

Calculate the standard deviation

4. Calculate the z-score

Determine the standard normal distribution using the formula above

FAQ

What is a standard normal distribution?

A standard normal distribution is also known as the z-score. It’s a normal distribution that has a mean of 0 and standard deviation of 1.