What is the peak - peak voltage of 15mV rms white noise?
Thermal noise (approximately white) has a gaussian distribution and we can use statistics to state what the probability is that a certain p-p level is exceeded: -



For instance in the diagram above a range of 6 sigma tells you that the probability of 1 V of noise remaining within the bounds of 6 Vp-p is 99.7% or put another way, 1 V RMS will remain below 6 Vp-p for 99.7% of the time.

It will also remain below 8 Vp-p 99.99% of the time.

Most engineers use 6.6 sigma - this produces a confidence level of 99.9% i.e. 1 V RMS remains within 6.6 Vp-p for 99.9 % of the time.

MT-048 page 5 from ADI is a useful reference for this: -



As for zener noise this article states that zener noise is "shot" noise and this article states it can be modeled as a Poisson process. This type of distribution can be very similar to a normal distribution: -



Picture taken from here. See also this article about the limiting cases for Poisson and normal distributions being the same.