Secondly, keep in mind also that all of the output probabilities are rounded (unless there is some lucky
coincidence). If you want the super exact value as a fraction, you need to use the formula by hand, or use a
different program such as wolframalpha.com.
Anyway, notice the three buttons below the n and p fields. Currently the middle one is selected, allowing us to
find the probability of X being between two constants, inclusive of the endpoints.
We can change the endpoints in three ways. (1) We can type them into the blanks in the probability statement
at the bottom. (2) We can click and drag the black triangles in the graph. (3) We can click and drag to highlight
rows in the table at the top right.
What if we just want the probability that X equals a single value? Just read that off of the table.
What if we want the probability that X is less than or equal to something? Choose the left button. And what if
we want the probability that X is greater than or equal to something? Choose the right button. You don’t have to
memorise that choice: notice how the shading of the graph changes.
For either of the latter two situations, i.e. a one-sided inequality, Geogebra can also help us solve the inverse
problem. That is, we can find the percentile. For example, let’s find the 80th percentile when n = 8 and p = .157.
Select the left button and type “.8” into the blank for the right-hand side of the probability statement at the bottom
(labelled “in” below) and hit enter.
After hitting enter, it actually changes to .8827 instead of .8 – this is not an error! The closest we can get is that
P(X ≤ 2) ≈ .8827, i.e. 2 is the 88.27th percentile. If n were higher, or if we were using some continuous distribution,
we could get closer to 80.