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Continuous uniform distribution?
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.
(A) What is the probability that a student sleeps between 10 and 14 minutes during a lecture?
(B) 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.
(C) How many lectures must a student attend to be 95% sure that they will have slept at least 28
minutes in total?
Use the quadratic equation to solve for the quadratic in question (C).
Hint: replace x with sqrt(n) to solve for n.