Normal distributions are quite common in real life settings.
A z-transformation changes a normal random variable with mean m and standard deviation s into a standard normal random variable with mean 0 and standard deviation 1. Any set of numbers has a mean and standard deviation. If we wanted to find out how many standard deviations a certain observation was from the mean, we would simply calculated its distance from the mean, and then divide by the standard deviation. For instance, consider the observation 5. In other words, the observation 5 is slightly more than one standard deviation below the mean.