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Standard Normal Distribution

Standard normal distribution is a normal distribution with mean equal to 0 and standard deviation of 1.

The general formula for the probability density function of the normal distribution is -
 


Where   μ = mean and σ = standard deviation.

When  μ = 0 and σ = 1, the probability density function becomes,
 

The normal random variable of a standard normal distribution is called standard score or z-score.

 

 

 

Properties of standard normal distribution:

1. The random variable z varies from -∞ to +∞.

2. The total area under the curve is equal to 1.

3. The curve is symmetric around 0.