Standard normal distribution
The standard normal distribution (SND) is a special case of the normal distribution. When a normally distributed variable has a mean of 0 and a standard deviation of 1, we call this distribution standard normal distribution.
The random variable is denoted by z. In other words, notice that we use z instead of x to represent the units for the SND. The units for the SND are called z values, z scores, standard units, or standard scores.
A z score of 2 is a point that has a value of z = 2 and it is two standard deviations to the right of the mean.
A z score of -1 is a point that has a value of z = -1 and it is one standard deviation to the left of the mean.
As we saw in the lesson about normal distribution, the total area under the standard normal curve is equal to 1.
Also because of symmetry, the area on either side of the mean is 0.5.
Notice that even though the z scores on the left of the mean are negative, the area under the curve is still positive.