if one has a Normal distribution with a mean of 50, the probability of any item/measurement/whatever having a value of exactly 50 is zero (or, more correctly, 'infinitely small').
Off topic I know, but are you sure that's correct?
Absolutely certain. However, you might call it "mathematical pedanticism", since it is only the "exactly" word which makes the statement true. The probability of an individual value from a Normal distribution being '
very close to' the mean of the distribution is high.
The frequency is wandering around 50Hz all the time, constantly passing through exactly 50Hz, so it's probably of being 50.000Hz at any moment is surely quite high! Just thinking out loud...
Think about this ... if one expresses the frequency to an 'unlimited' number of decimal places, then there is an infinite number of values it could take, even over a small range (e.g. 49 - 51 Hz). That means that the probability of any individual item from that Normal distribution having
any one of that infinite number of possible values (just one of which infinite number of possibilities is 'exactly 50') is infinitely small (aka 'zero'). Nor is there anything special about the mean (50) - the probability of the actual value being
exactly equal to any value (e.g. 50.123456) is also infinitely small.
However, again, as above, this is of theoretical relevance only. Get rid of that word 'exactly' and the probability of the frequency being 'very close to 50 Hz' is very high, not zero! Even the probability of the frequency being 'incredibly close to 50Hz' is high. It's only "exactly 50 Hz" which causes the theoretical mathematical issue.
Kind Regards, John