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

To calculate the standard normal distribution, subtract the mean by the normal random variable, then divide by 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. \