If an analyst's forecast can increase the project's expected value by $5,$ from $12$ to $17,$ while perfect information can increase the project's expected value by $8,$ from $12$ to $20,$ then...what is the efficiency of the sample information?

$E=\frac{5}{8}$

$E=\frac{12}{17}$

$E=\frac{17}{20}$

$E=\frac{5}{20}$