A Museum Only Allows Patrons to Enter at Fifteen Minute $8$

Multiple Choice

A museum only allows patrons to enter at fifteen minute intervals. An observer notices that every weekday at 2:00 there are $8$ people waiting at the entrance and at 3:00 there are $20$ people waiting. In addition, there are $10$ people waiting at the entrance at all 15-minute intervals that are not on the hour. This pattern continues through 6:00. How many people wait to enter the museum in the interval from 2:00 to 6:00?

A) $280$
B) $232$
C) $291$
D) $248$
E) $208$