Probability question, using a graphing calculator 22% of the Dutch population goes on a vacation in the Netherlands, 36% goes abroad for a vacation and 14% goes on a vacation in the Netherlands, and also goes abroad. The rest doesn't go on a vacation. A research is conducted with 80 Dutch participants, calculate the chance that between 20% and 30% goes on vacation exclusively abroad (allowed to use a graphing calculator with binomcdf). I thought you could just do: $P (X \leq 24) - P (X \leq 16)$ = binomcdf (80 (# of trials), 0.36 (p), 24(# of succesfull trials) - binomcdf (80, 0.36, 16). My textbook however says that it is: $P (X \leq 23) - P(X \leq 16)$. Why is this?

There would be a good argument for $\Pr(X\le 24)-\Pr(X\le 15)$. This includes both endpoints. In ordinary mathematical English (but this problem may not have been originally in English) the case for $\Pr(X\le 23)-\Pr(X\le 16)$ is I think weaker.

The answer you suggest, $\Pr(X\le 24)-\Pr(X\le 16)$, seems less reasonable: Implicitly, that includes the $30\%$ end point, but excludes the $20\%$ end point. An interpretation that either includes both or excludes both is easier to justify.