The reason why a Gaussian makes sense is because noise is often the result of summing a large number of different and independent factors, which allows us to apply an important result from probability and statistics, called the cen tral limit theorem.

Is noise normally distributed?

Many physical noise mechanisms are Normally distributed. It also tends to admit closed form solutions.

Is white noise always Gaussian?

Noise having a continuous distribution, such as a normal distribution, can of course be white. It is often incorrectly assumed that Gaussian noise (i.e., noise with a Gaussian amplitude distribution – see normal distribution) necessarily refers to white noise, yet neither property implies the other.