The standard normal distribution is unimodal and symmetrically distributed with a bell-shaped curve. Normal Distribution VS Standard Normal Distribution Read More: Mean and Variance of Random Variable The following formula can be used to convert any normal random variable X into a z score: The random variable of a standard normal curve is referred to as the standard score or a Z-score. Standard Normal Distribution is a kind of normal distribution that appears when a normal random variable has a mean value equals to zero and the value of standard deviation equals one.