The price of an item in a project supply store is a random variable having the following distribution:

\[ f(x)=\left\{\begin{array}{cl} \frac{1}{20} \sin ^{2}\left(\frac{\pi(x-35)}{10}\right), & 35 \leq x \leq 75 \\ 0, & \text { otherwise } \end{array}\right. \]

Which of the following price ranges has the highest probability? [35, 36]; [50, 51]; \([68,69]\)