I need to understand an explanation from a
swirl() lesson in a course on "Statistical Inference", menu option "Probability2". At 76% of completion, there is a question:
The quantile v of a CDF is the point x_v at which the CDF has the value v. More precisely, F(x_v)=v. A percentile is a quantile in which v is expressed as a percentage.
What percentile is the median?
The answer is "50th"... ok...
Right after, there is another question:
What is the 50th percentile of the CDF F(x)=(x^2)/4 from the example above?
I know from here, the answer is $1.414214$, but I cannot find the reasoning to reach the result. I'm not sure if it is just a simple semantics catch, but I'm finding hard to understand how to reach the answer. Any idea or help?