Clarification on Calculation of Interval in Chapter 2

[OrtizNicola]

In Chapter 2, the author states:

"With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.05 to 0.35 (marked by the solid lines)."

I am trying to understand how these values (0.05 to 0.35) are calculated. I initially thought they were derived from the Highest Density Interval (HDI), but the HDI is from 0 to 0.42.

Can someone provide an explanation of how to calculate the 0.05 to 0.35 interval mentioned in the book? Any pointers or detailed steps would be greatly appreciated.

Thank you!

[miba2020]

I also want to know where these numbers come from.

Now I think 0.05 and 0.35 might have their roots in the plot. Something like majority of mass falling in the range of [0.05, 0.35]. After reading chapter 3, I try az.plot_posterior with hdi_prob=0.8, then I get a plot saying 80% hdi lies between 0.042 and 0.35.

Don't know whether the above guess is correct or not. But I decide to read on later chapters in the hope of things will get clear thereafter.