After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only five women among the last 17 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 five or fewer women when 17 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).
P(at most five) = 



We can approach this problem using the binomial distribution. Since there are equal numbers of qualified men and women, we can assume that each hire is equally likely to be a man or a woman, giving a probability of \( p = 0.5 \) for each individual hire to be a woman.

The binomial distribution formula is:

\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]

where:
- \( n = 17 \) (the total number of hires),
- \( p = 0.5 \) (the probability of hiring a woman),
- \( k \) is the number of women hired (in this case, we are looking for \( k \leq 5 \)).

We need to calculate the cumulative probability for hiring 5 or fewer women, that is:

\[
P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
\]

I'll calculate the required probabilities and sum them up.The probability of hiring 5 or fewer women when 17 people are hired, assuming no gender discrimination, is approximately \( 0.07173157 \) (accurate to 8 decimal places).

Do you have any questions or would you like more details on how this was calculated?

Here are 5 related questions to further explore the topic:
1. What is the probability of hiring exactly 5 women?
2. How does the binomial distribution apply to other real-world hiring scenarios?
3. What would the probability be if the company hired 20 employees instead of 17?
4. How can the cumulative probability be used in statistical testing for discrimination?
5. What assumptions must hold true for the binomial model to be valid in this scenario?

**Tip:** The binomial distribution is useful for calculating probabilities when there are only two possible outcomes (like male or female in hiring). It's often used in situations involving trials with fixed probabilities.

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only five women among the last 17 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 five or fewer women when 17 people are hired, assuming that there is no discrimination based on gender. (Report answer accurate to 8 decimal places). P(at most five) = 

Find the probability of hiring 5 or fewer women when 17 people are hired, assuming no gender discrimination. This problem applies binomial distribution to a real-world scenario, focusing on key concepts in probability theory and cumulative probability. Ideal for students in Grades 10-12.

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