How Do You Calculate Binomial Probabilities for Survey Representation?

In summary: This will also assure our helpers that you are not just trying to cheat on your homework, as the help we give is meant as a supplement to your own efforts, not as a substitute for them.In summary, the conversation is about a person asking for help with a problem and clarifying that they are not trying to cheat. The problem involves selecting a random sample of students and ensuring that the proportion of minority students in the sample is approximately 10%. The conversation also includes a request for the person to show their progress and thoughts on the problem.
  • #1
kwiddoes23
2
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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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  • #2
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?
 

FAQ: How Do You Calculate Binomial Probabilities for Survey Representation?

What is a binomial distribution?

A binomial distribution is a probability distribution that describes the outcomes of a binary (two possible outcomes) experiment. It is characterized by two parameters, n and p, where n is the number of trials and p is the probability of success for each trial.

How is a binomial distribution different from a normal distribution?

A binomial distribution is discrete, meaning that it only takes on whole number values, while a normal distribution is continuous, meaning that it can take on any value. Additionally, a binomial distribution is characterized by two parameters, while a normal distribution is characterized by mean and standard deviation.

What is the formula for calculating a binomial probability?

The formula for calculating a binomial probability is P(x) = (nCx) * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successes, and p is the probability of success for each trial. (nCx) represents the combination formula, n!/(x!(n-x)!).

Can a binomial distribution be used for non-binary outcomes?

No, a binomial distribution is specifically used for experiments with two possible outcomes. If there are more than two outcomes, a different distribution, such as a multinomial distribution, should be used.

How is a binomial distribution used in real-life situations?

Binomial distributions can be used to model real-life situations that involve binary outcomes, such as flipping a coin, rolling a die, or testing the success rate of a new medication. They can also be used to predict the likelihood of a certain number of events occurring in a given number of trials.

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