Remember that the distribution looked like a right triangle.

In the distribution function, for example if wanted to

find the probability that x proportion of calls got answered on a given day or less,

that F of x, that distribution function, worked out to simply be x squared.

Where x has to be a value between 0 and 1 for it to make sense.

In this case, we want to solve 0.5 equals F of x, which is equal to x squared.

Resulting in the solution square root 0.5.

This is 0.7.

So what this means is that on about 50% of the days,

70% of the phone calls, or fewer get answered.

And on about 50% of the days, about 70% of the phone calls or more get answered.

We work with quantiles a lot, especially quantiles from the normal distribution.

We almost never go through this process of working directly with the densities to

calculate quantiles, because the distributions we work with are common and

this has already been done for us.

In R, there's an easy tri-,

trick.

Basically, q in front of the function name,

function density name, gives the quantiles.

So in this case, we know that this is a beta density.

Well, we don't know.

I'm telling you that this is a beta density.

And so qbeta gives us the relevant quantile.

Here we plug in 0.5.

And remember R takes the argument of the quantile as a proportion.

So, if you plug in 0.5, it will work.

If you plug 50 for 50%, it will not work.

Okay, and the 2 and

the 1 are the parameters that we haven't really fully described.

But that you are going to have to just take my word for it that those

are the parameters that yield the specific data density that we're looking at.

And when we plug this in, we get 0.7, 0.71, exactly like we got before.