The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The standard normal distribution is centered on zero and the extent to which a given measurement deviates from the mean is given by the standard deviation. For the standard normal distribution, 68% of the observations lie within 1 standard deviation of the mean. 95% lie within two standard deviations of the mean and 99.9% lie within 3 standard deviations of the mean. Up to this point, we have used “X” to denote the variable of interest eg, X=BMI, X=height, X=weight. However, when using the standard normal distribution, we will use "Z" to refer to the variable in the context of the standard normal distribution. After standardization, BMI=30 discussed on the previous page shows 0.16667 units above the mean of 0 on the standard normal distribution at the bottom right.