MATH125 students must attend $t$ hours, where $t ∈ [0, H]$, of lectures and pass four obligatory exercises to qualify for the end of semester examination. The number of students who attended between $t_1$ and $t_2$ hours of lectures is described by the integral
$$\int^{t_2}_{t_1} 20t^2dt ,\qquad 0≤ t_1 < t_2 ≤ H$$
Some students attended less than $H/2$ hours of lectures and passed the obligatory exercises so they are qualified to take the examination.
Find the ratio of students who attended less than $H/2$ hours of lectures