Seems I found the solution.
Let n be the number of trials, π₀ be the reference probability. (I denote it with π to avoid confusing with p-value that will be mentioned later.) Let p₀ be the threshold probability from my original post. Then a dynamic array of all values for which the distribution is no greater than p₀ can be generated by the formula
This works with Excel versions that support dynamic arrays and corresponding functions like FILTER and SEQUENCE.
But finding these values was not an end in itself for me; this was in fact needed to calculate an exact binomial p-value for two-sided proportion test: k is the observed number of successes, π = k/n is the sample proportion, and the hypotheses are:
So the p-value for this test can be calculated by the formula shown at this screenshot, and the corresponding Excel file is also attached.
binomial_p-value.png
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