Jacob Bernoulli, Binomial Distribution, Probability, Central Limit Theorem, Deep Dives.
the mean water quality of any of these 50 random samples is X_bar_n. Effectively, you ended up with 50 random values of X_bar_n. Clearly, X_bar_n is a random variable. Importantly, any one of these X_bar_n values is your estimate of the unknown — and never will it ever be known — true, average