Help on Binomials! ASAP

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Enam

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Having a hard time conceptualizing this or trying to begin setting up the problem.

Take a sample of five students from out class of 38. Of the 38, 4 students are above age 30. You want to choose the sample size “k” in such a way that the mean age of the sample is not too skewed toward the older students.Treat the selections as independent binomial probabilities. In particular, there should be no more than a 10% chance that 1/5 or more of the sample contains any of these four tall students.

For values of k = 1 to 20, what is the limit to the number of tall students in the sample?






Choose two values of k that have the same limit. When k increases, but the limit does not, does the chance of having too many tall students in the same increase or decrease? Show your calculations.







Based on (b), should you consider the lowest or highest values of k with the same limit?



Following (c), state the value of k to use, and show your calculations.
 
Enam said:
Take a sample of five students from out class of 38. Of the 38, 4 students are above age 30. You want to choose the sample size “k” in such a way that the mean age of the sample is not too skewed toward the older students. Treat the selections as independent binomial probabilities. In particular, there should be no more than a 10% chance that 1/5 or more of the sample contains any of these four tall students.

For values of k = 1 to 20, what is the limit to the number of tall students in the sample?

Choose two values of k that have the same limit. When k increases, but the limit does not, does the chance of having too many tall students in the same increase or decrease? Show your calculations.

Based on (b), should you consider the lowest or highest values of k with the same limit?

Following (c), state the value of k to use, and show your calculations.
Click to expand...
What is "(b)"? What is "(c)"? (There are no such designators in your post.) Is there an "a" or a "d"?

What is the point of the height of the students, when you've only been given information on, and told to choose based upon, students' ages?

What are your thoughts on this? What have you tried? How far have you gotten? Where are you stuck? Or are you unable even to begin, and need lesson instruction first?

Please be complete. Thank you! ;)
 
stapel said:
What is "(b)"? What is "(c)"? (There are no such designators in your post.) Is there an "a" or a "d"?

What is the point of the height of the students, when you've only been given information on, and told to choose based upon, students' ages?

What are your thoughts on this? What have you tried? How far have you gotten? Where are you stuck? Or are you unable even to begin, and need lesson instruction first?

Please be complete. Thank you! ;)
Click to expand...

There's typo in A and B. It should read "old" students. Trying to find the limit to old students in the sample.

Sorry the copy and pasting not going so well. But (a) For values of k = 1 to 20, what is the limit to the number of old students in the sample? (b) Choose two values of k that have the same limit. When k increases, but the limit does not, does the chance of having too many older students in the same increase or decrease? Show your calculations. (c) Based on (b), should you consider the lowest or highest values of k with the same limit? and (d) Following (c), state the value of k to use, and show your calculations.

I read the question as taking samples of 1 - 20. So those are your N values. For those samples I said that for K value of 1-9, we couldn't have any students as they would break the rule where we wanted to have them be 10% of the sample. And values 10 - 19, you could have one of these older students as 1/10 - 1/19 gives you less than 10%. and for value 20 I said only 2 could be present as 2/10 = 10% or less.


For (b) i calculated from sample of 10 and 11 so I did binomial of 10 choose 1 and 11 choose 1 because you only want one student in the sample. and got answer where as k increases, the probability decreases.

I'm hoping to have read it correctly and am on track of doing this problem correctly and would like thoughts if someone read it differently or I am completely wrong on approaching this.

 
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