is your $\alpha_2$ quantile of the population mean?
       $\theta$       Suppose the population mean is known to be $\hat{m}$. Then let $\theta$ denote the proportion of members of population that will lie in the interval $[\hat{m}, \hat{m}+c]$.
   $\theta_{(0.05)}$  What is your 5th percentile of the unknown proportion $\theta$ that will lie in the given interval?
   $\theta_{(0.95)}$  What is your 95th percentile of the unknown proportion $\theta$ that will lie in the given interval?

  : The elicitation questions with the corresponding notation.[]{data-label="tab:elicited-questions"}

### Choice of $c$

Theoretically, regardless of the choice of $c$, the expert will have a 5th and 95th percentile for her corresponding proportion $\theta$, from which the hyperparameters $a$ and $b$ can be determined. However, the expert may find the elicitation task particularly difficult for certain choices of $c$, for example, for sufficiently large $c$, the expert may simply be certain that $\theta$ will be 0.5. In any case, there is likely to be some vagueness to the expert’s judgements: for example, she may state $\theta_{(0.95)}=0.4$, but express indifference to an alternative value such as 0.35. Hence, in practice, some choices of $c$ may be better than others, both in helping the expert to consider her percentiles for $\theta$, 