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

Standard Normal Distribution Definition

Standard normal distribution is a measure of the normal distribution with a mean of 0.

How to calculate a standard normal distribution?

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


What is a standard normal distribution?

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