MHB How Do You Calculate Binomial Probabilities for Survey Representation?

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To calculate binomial probabilities for survey representation, the problem involves determining the likelihood that international students, who make up 10% of a population, are represented in a sample of size n=100 and n=1000 within a range of 8-12%. The user seeks guidance on setting up the calculations without asking for direct answers. It is suggested that sharing initial attempts or thoughts would help others provide more targeted assistance. Understanding the binomial distribution and applying it to the given sample sizes is crucial for solving the problem effectively.
kwiddoes23
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Hello, I was hoping someone could help explain how to do this problem. I have been stuck on it for a while now. I know that you have to use a binomial with n=100, then n=1000 but I'm not sure how to set it up to solve for a range from 8-12%. Thanks! Any advice is appreciated. Also, for people just out to block questions, I AM NOT ASKING FOR THE ANSWER - I AM NOT TRYING TO CHEAT. I just would like help.

Suppose in a large pool of students, 10 % are international students. We are going to randomly select n students to conduct a survey. We are concerned about international students being either over-represented, or under-represented in the survey. Ideally, the proportion of the minority students in the selected group should be 10 %.

(a) If n is 100, what is the probability that this type of minority students are reprented
in the survey by approximately correct proportion (8 to 12%) ?

(b) if n is 1000, what is the probability that this type of minority students are
reprented in the survey by approximately correct proportion (8 to 12%) ?
 
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Hello kwiddoes23 and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

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