How Do You Calculate Binomial Probabilities for Survey Representation?

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SUMMARY

This discussion focuses on calculating binomial probabilities for survey representation, specifically for a population where 10% are international students. The problem involves determining the probability of selecting a sample of size n=100 and n=1000 that accurately reflects this proportion within the range of 8% to 12%. The discussion emphasizes the importance of setting up the binomial distribution correctly to solve for these probabilities.

PREREQUISITES
  • Understanding of binomial distribution and its parameters
  • Familiarity with probability calculations
  • Knowledge of statistical sampling methods
  • Basic skills in using statistical software or calculators
NEXT STEPS
  • Learn how to apply the binomial probability formula for different sample sizes
  • Explore the Central Limit Theorem and its implications for large sample sizes
  • Study how to use statistical software like R or Python for binomial probability calculations
  • Investigate confidence intervals for proportions in survey data
USEFUL FOR

This discussion is beneficial for statisticians, data analysts, and researchers involved in survey design and analysis, particularly those focusing on representation of minority groups in sample populations.

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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