Lets say for example you are a student in a physics class and the professor states that the distribution of grades on the first exam throughout all sections was a binomial distribution. With typical class averages of around 40 to 50 percent. How would you interpret that statement?
Most likely the professor was talking loosely and his statement
means that the histogram of percentage scores resembled the
bell-shaped curve of a normal density function with average or
mean value of $40\%$ to $50\%$. Let us assume for convenience
that the professor said the average was exactly $50\%$. The
standard deviation of scores would have to be at most $16\%$
or so to ensure that only a truly exceptional over-achiever
would have scored more than $100\%$.
As an aside, in the US, raw scores on the GRE and SAT are
processed through a (possibly nonlinear) transformation so
that the histogram of reported scores is roughly bell-shaped
with mean $500$ and standard deviation $100$. The highest
reported score is $800$, and the smallest $200$. As the saying
goes, you get $200$ for filling in your name on the answer sheet.
At the high end, on the Quantitative GRE, a score of $800$ ranks
only at the $97$-th percentile.
What if the professor had said that there were no scores that were
a fraction of a percentage point, and that the histogram of
percentage scores matched a binomial distribution with mean $50$
exactly? Well, the possible percentage scores are $0\%$,
$1\%, \ldots, 100\%$ and so the binomial distribution in question
has parameters $(100, \frac{1}{2})$ with $P\{X = k\} = \binom{100}{k}/2^{100}$.
So, if $N$ denotes the number of students in the course, then
for each $k, 0 \leq k \leq 100$, $N\cdot P\{X = k\}$ students had a percentage score of $k\%$.
Since $N\cdot P\{X = k\}$ must be an integer, and
$P\{X = 0\} = 1/2^{100}$, we conclude that $N$ is an integer
multiple of $2^{100}$. I am aware that physics classes are often
large these days,
but having $2^{100}$ in one class, even if it is subdivided
into sections, seems beyond the bounds of
plausibility! So I would say that your professor had his tongue
firmly embedded in his cheek when he made the statement.