Hypergeometric Distribution homework problem

In summary, the conversation discusses the probability of 6 women out of 10 individuals below the median salary in a group of 20 employees. The formula used is given as (r choose x) ((n-r) choose (n-x)) / (N choose n), with N = 20, n = 10, r = 7, and x = 6. The logic behind this approach is to consider the 10 individuals below the median as a random sample from the group of 20, with 7 women in the group. The conversation ends with the suggestion to use the given formula to solve the problem.
  • #1
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Homework Statement



A large company employs 20 individuals as statisticians, 7 of whom are women and 13 of whom are men. No two people earn the same amount.

What is the probability that 6 of the women earn salaries below the median salary of the group?

Homework Equations



If r is the number of "successes" in a set of N element, and x is the number of success in n elements draw, then p(x) = (r choose x) ( (n - r) choose (n - x) ) / (N choose n).

The Attempt at a Solution



I'm pretty sure that I just plug & chug with N = 20, n = 10, r = 7, x = 6. But I'm not 100% sure about the logic of all this. So, we look at the 10 persons below the median, who, for all we know, are just 10 random people from the group of 20. We know that there are 7 women in the group of 20, and we want to know the probability that 6 of our 10 random persons are women. Is that right? I feel a little thrown-off by the "median" thing.
 
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  • #2
I am probably not the best source for this question but I have the same exact logic as you on this problem. The sample size is 20 (which is N). 7 out of the 20 you would consider sucesses (which is r). You are selcecting 10 people at random from the the 20 because that is how many there is below the median (which is n), and you want there to be exactly 6 successes out of the 10 (which is x). So I say plug and chug the way you have it.
 

What is the Hypergeometric Distribution?

The Hypergeometric Distribution is a probability distribution that describes the likelihood of obtaining a certain number of successes in a specific sample, given a known population size and number of successes in the population. It is often used to analyze situations where the sample is taken without replacement, such as drawing cards from a deck.

How do you calculate the probability in a Hypergeometric Distribution?

The formula for calculating the probability in a Hypergeometric Distribution is: P(X = x) = (NcX)(N-nc-nX)/(NX), where N is the population size, n is the sample size, c is the number of successes in the population, and x is the number of successes in the sample.

What is the difference between a Hypergeometric Distribution and a Binomial Distribution?

Both the Hypergeometric Distribution and the Binomial Distribution are used to analyze situations involving a fixed sample size and a known number of successes. The key difference is that the Hypergeometric Distribution is used when the sample is taken without replacement, while the Binomial Distribution is used when the sample is taken with replacement.

How do you use the Hypergeometric Distribution to solve a homework problem?

To solve a homework problem involving the Hypergeometric Distribution, you first need to identify the values for N, n, c, and x. Then, plug these values into the formula P(X = x) = (NcX)(N-nc-nX)/(NX) and solve for P(X = x). Finally, interpret the result in the context of the problem.

What are some real-life applications of the Hypergeometric Distribution?

The Hypergeometric Distribution is commonly used in genetics, quality control, and market research. For example, it can be used to predict the likelihood of certain traits being passed down in a population, the probability of a batch of products meeting quality standards, or the chance of a specific demographic being targeted in a marketing campaign.

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