After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only four women among the last 21 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.

Help her address the charge of gender discrimination by finding the probability of getting four or fewer women when 21 people are hired, assuming that there is no discrimination based on gender.
*(Report answer accurate to 8 decimal places).*
*P*(at most four) =

Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge?

yes, this supports a charge of gender discrimination

no, this does not support a charge of gender discrimination

To help Kim address the gender discrimination issue, we can model the situation using the **binomial distribution**.

Given:
- The probability of hiring a woman, \( p = 0.5 \) (since there's no bias between men and women, the probability is equal for both).
- The number of hires, \( n = 21 \).
- The number of women hired, \( k \), is what we're interested in (finding the probability of hiring **at most 4** women).

The binomial probability mass function is:
\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]
Where:
- \( \binom{n}{k} \) is the binomial coefficient, representing the number of ways to choose \( k \) women out of \( n \) hires.
- \( p \) is the probability of hiring a woman (0.5).

We are asked to find the probability of hiring 4 or fewer women out of 21 hires. This can be written as:
\[
P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
\]
Let's calculate this cumulative probability.The probability of hiring **at most 4 women** out of 21 hires, assuming no gender discrimination, is approximately \( 0.00359869 \) (or about 0.36%).

Given that this probability is less than the 0.5% cutoff value (0.005), it suggests that this event is quite unusual and could support a claim of gender discrimination.

Thus, the result **supports a charge of gender discrimination**.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How is the binomial distribution used in hypothesis testing?
2. What are Type I and Type II errors in the context of discrimination claims?
3. How would the conclusion change if the cutoff value was 1% instead of 0.5%?
4. How does the sample size affect the likelihood of extreme outcomes like this?
5. Can we apply other statistical tests to support or refute this claim?

**Tip:** When evaluating rare events, a smaller p-value or probability indicates stronger evidence against the assumption of fairness.

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only four women among the last 21 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. Help her address the charge of gender discrimination by finding the probability of getting four or fewer women when 21 people are hired, assuming that there is no discrimination based on gender. (Report answer accurate to 8 decimal places). P(at most four) = Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge? yes, this supports a charge of gender discrimination no, this does not support a charge of gender discrimination

Explore the application of binomial distribution to assess gender discrimination claims. Learn how to calculate the probability of hiring four or fewer women out of 21 employees, assuming no gender bias. This problem involves key concepts in probability theory, binomial distributions, and hypothesis testing. Suitable for advanced high school or undergraduate students.

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