During my first year of teaching at Q, I had a class with an official enrolment of 350 students, but the lectures were scheduled in a room that had a maximum capacity of 160. When I queried the timetabling department, they told me the chance a typical Q student goes to a lecture is 40%.

a) Using normal approximations both with and without the continuity correction, estimate the probability my room was too small to hold the audience for one of my lectures.

b) During the mid-semester exam period, students were even less likely to attend lectures. In these circumstances, do you think the normal approximation for the chance the room is too small will be better or worse than it was for part (a)?Briefly justify your answer.