Probability, Expected Vaulue, Standard Deviation: 2 Questions

bran

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Mar 2, 2015
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Hello,
It would be great if you could help me with my two problems, as I have an exam pretty soon. Many thanks in advance. :)

1.
Questions 1->3 were relatively easy to answer but I’m stuck at 4.

The cafeteria of a school has two meals on the menu: Meal I and Meal II.
338 students eat at the cafeteria; all of them have either Meal I or meal II. Experience tells that they will pick Meal I with probability 0.4. (We assume an independent choice).

  1. Calculate the expected values for each meal.
  2. How many meals of each kind must be available if the probability that somebody does not get the meal he or she wanted is to be smaller than 2.3%.
  3. The manager of the cafeteria decides to prepare just 10 extra helpings. How many of them should be Meal I, and how many should be Meal II?
  4. Based on your answer to part 3), calculate the probability that all students get the meal they want.
My answers so far:

  1. E[MI] = 135.2; E[MII] = 202.8
  2. To reduce the probability of running out to 2.3% we need to add 2 standard deviations.
σ=(n*p*q)^0.5= ca. 9
--> We need 153 helpings of Meal I and 221 helpings of Meal II.
3. Both Meal have same standard deviation, it makes sense to split the 10 extra helpings evenly on Meal I and II; 5 extra helpings of each.
4. … That’s the question. Don’t know hot to.

2.
A coin has a probability of 0.486 to come up “heads”.
How many times do we have to toss the coin until a 50:50 in the category of “typical behaviour”.
I’m not sure whether typical behaviour is +/- 1 or 2 σ from the mean, but how to solve the whole thing, the approach etc is the main problem.

I’d be very glad if you could help me.

P.S.: If you now a place/site to find exercises like these (but with answers), please tell me. Google doesn't deliver great results.
 
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