Sorry Prof, but the standard deviation is an OBSERVED FACT and not
a fixed mathematical notion. It is a measure of dispersion of the
data in the samples.
In the model example, if you only have three NP box cars out of a set
of 100, and your trains are all 33 cars long, then you cannot experience
the REAL WORLD possibility of trains having 33 NP box cars (or 32, or 31,
etc). Moreover, the probability that your 33 car trains will have at
least one NP box car in them is much higher than it is on the prototype!
(See Einstein, Same Birthdays Probability Among 50 Strangers.)
It is as I stated, the Variance (the term I prefer) of the prototype is
greater than the Variance of the model. (Variance simply being the square
of the Standard Deviation.)
The MEAN number of NP box cars in the 33 car trains is 1, in both the
model and prototype.