I suggest using the Central Limit Theorem.Hey all, this is from a past exam but we were not given any solutions.

The Question:

Many students find that sitting through an entire lecture is difficult to do without falling asleep. Suppose the number of minutes a single, randomly selected student is asleep during a lecture is uniformly distributed between 7 and 14 minutes.

1.) Over the course of the semester (say, 50 lectures), what is the probability that a randomly selected student will sleep a total of between 130 and 140 minutes?

Assume that the minutes slept in any lecture is independent of the number of minutes slept in any other lectures.

2.) How many lectures must a student attend to be 95% sure that they will have slept at least 28 minutes in total?

I have done previous parts to the question that ask for E(X) and Std Deviation but I can't work out these 2.

Any help would be appreciated.

Thanks