Finding an unknown in a formula

The heights of some students are grouped as follows.

- $140 < x \le 145$: 3 students
- $145 < x \le 150$: $p$ students
- $150 < x \le 155$: 12 students
- $155 < x \le 160$: 9 students
- $160 < x \le 165$: 4 students

Given that the median class is $150 < x \le 155$, write down the largest possible value of $p$.