A survey showed that 32% of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 25 human resource professionals are randomly selected, would 14 be a significantly high number to be at companies that rejected job candidates because of information found on their social media? Why or why not?
Select the correct choice below and fill in the answer box within your choice.
(Round to four decimal places as needed.)
• A. Yes, 14 would be significantly high because the probability of 14 or more is , which is low.

O B. No, 14 would not be significantly high because the probability of 14 or more is , which is not low.

• c. Yes, 14 would be significantly high because the probability of 14 or more is , which is not low.

O D. No, 14 would not be significantly high because the probability of 14 or more is , which is low.

To solve this, we need to calculate the probability that 14 or more human resource professionals out of 25 would work for companies that rejected job candidates based on social media information, given that 32% of HR professionals are in such companies. This situation can be modeled using a binomial distribution with the following parameters:

- \( n = 25 \) (the number of HR professionals selected)
- \( p = 0.32 \) (the probability of a single HR professional being at a company that rejects candidates based on social media)
- \( x = 14 \) (the number of HR professionals who rejected candidates based on social media)

The binomial distribution formula for finding the probability of exactly \( k \) successes out of \( n \) trials is given by:

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

However, in this case, we are interested in the cumulative probability of getting 14 or more HR professionals in such companies. We can compute the cumulative probability \( P(X \geq 14) \).

Let me calculate the probability.The probability of 14 or more HR professionals being at companies that reject job candidates based on social media information is approximately \( 0.0112 \), or 1.12%. 

Since this probability is quite low (less than 5%), 14 HR professionals would be considered a significantly high number.

The correct answer is:

**A. Yes, 14 would be significantly high because the probability of 14 or more is 0.0112, which is low.**

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Do you want more details or have any further questions?

Here are 5 related questions for further exploration:
1. What is the probability of exactly 14 HR professionals being at such companies?
2. How would the result change if the probability of rejection based on social media were 40% instead of 32%?
3. What is the expected number of HR professionals out of 25 to be at companies that reject candidates based on social media?
4. What would be considered a "significantly low" number of HR professionals for this scenario?
5. How does increasing the sample size to 50 HR professionals affect the probability?

**Tip:** When dealing with binomial probabilities, always check the cumulative probability for values above or below a threshold to determine significance.

A survey showed that 32% of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 25 human resource professionals are randomly selected, would 14 be a significantly high number to be at companies that rejected job candidates because of information found on their social media? Why or why not? Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) • A. Yes, 14 would be significantly high because the probability of 14 or more is , which is low. O B. No, 14 would not be significantly high because the probability of 14 or more is , which is not low. • c. Yes, 14 would be significantly high because the probability of 14 or more is , which is not low. O D. No, 14 would not be significantly high because the probability of 14 or more is , which is low.

Explore whether 14 out of 25 human resource professionals at companies rejecting candidates based on social media is a significantly high number, using binomial distribution and cumulative probability calculations. Learn key probability concepts and how to calculate the probability for this scenario. Suitable for students in Grades 10-12.

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