## anonymous 5 years ago question in the reply :)

1. anonymous

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. 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 this question. Hint: replace x with sqrt(n) to solve for n.

2. M

3. anonymous

im not sure what the equation is, thats the problem

4. M

then you can't solve those questions unfortunately

5. M

maybe you can lol

6. anonymous

ye i tried. not sure how tho.

7. M

formula is $1/(\beta - \alpha)$

8. M

1/(14-7)

9. anonymous

r u sure? thats what i used for the first part of this question. this part seems more complicated?

10. M

1/7 for 7 < x < 14

11. M

1/7x from 7 to 14

12. M

if you integrate that formula i gave you then it becomes 1/7 (x) you follow up to that?

13. M

i mean 1/7(x) from 130 to 140 mins

14. anonymous

ohkay

15. anonymous

so the sample size 50 goes where?

16. M

you have the final answer by any chance

17. anonymous

lol no i dont

18. M

the number of lecture should matter because it's uniform random variable

19. M

so answer should be approx. 1.4286

20. anonymous

how do u get that?

21. M

you integrate 1/7 you get (1/7)x then you take the limit from 140 to 130

22. M

are you sure it's 140 and 130 mins?

23. anonymous

yeah it is

24. M

hmm maybe you're supposed to divide the minutes by 50 lectures

25. anonymous

maybe haha.

26. M

i think you're supposed to do that then you get .02857 = 2.857%

27. anonymous

ok. wud u be able to tell me how u got the limit form 130 to 140?

28. M

you first divide 140/50 and 130/50 to get 2.8 and 2.6

29. M

then you (1/7)(2.8) - (1/7)(2/6) = .0287

30. M

(1/7)(2.8) - (1/7)(2.6) = .0287

31. anonymous

ohh okay.thanks :) do u kno how to do parrt C?

32. M

not sure since i didn't learn this using quadratic only hypergeometric :( sorry

33. M

and binomial

34. M

look at your notes and set it equal to .95

35. M

good luck

36. anonymous

kays np. thanks for ur help :)

37. anonymous

lol theres a medal for u :)