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
- 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.
- Determine the average
Calculate the mean or average of the data set
- Determine the standard deviation
Calculate the standard deviation
- 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.
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