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To solve this problem, we need to determine whether 16 human resource professionals out of 27 is a significantly high number for rejecting job candidates based on information found on social media. The key is to analyze this using a **binomial probability distribution** since the outcome is binary: either a professional is at a company that rejects candidates based on social media or they are not.

### Step-by-Step Breakdown:

1. **Given Information:**
   - Probability (\(p\)) that an HR professional is at a company rejecting candidates based on social media: 0.37.
   - Sample size (\(n\)): 27.
   - Number of successes (\(x\)): 16.

2. **Calculate the mean (\(\mu\)) and standard deviation (\(\sigma\)) for the binomial distribution:**
   \[
   \mu = n \times p = 27 \times 0.37 = 9.99 \approx 10
   \]
   \[
   \sigma = \sqrt{n \times p \times (1 - p)} = \sqrt{27 \times 0.37 \times 0.63} = \sqrt{6.2901} \approx 2.51
   \]

3. **Determine if 16 is significantly high:**
   - A value is considered "significantly high" if it is more than 2 standard deviations above the mean.
   \[
   \mu + 2\sigma = 10 + 2 \times 2.51 = 10 + 5.02 = 15.02
   \]
   Since 16 is slightly above 15.02, we can consider 16 to be **slightly higher than two standard deviations above the mean**, indicating it may be significantly high.

4. **Probability calculation:**
   To precisely determine if 16 is a significantly high number, we would calculate the binomial probability of obtaining 16 or more successes out of 27 trials. This involves summing the probabilities from \(P(X = 16)\) to \(P(X = 27)\).

### Conclusion:
Without calculating the exact binomial probability, based on the mean and standard deviation, **16 is likely to be a significantly high number** because it exceeds two standard deviations from the mean. Therefore, the most appropriate answer would be **Option B: Yes, 16 would be significantly high because the probability of 16 or more is low**.

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Would you like a detailed probability calculation or further clarification?

Here are 5 follow-up questions:
1. What is the exact probability of getting 16 or more successes in this scenario?
2. Can you calculate the cumulative probability for different values of \(x\)?
3. How does the standard deviation affect the interpretation of significance?
4. What would be considered a significantly low number in this scenario?
5. How would the conclusion change if the probability \(p\) were different?

**Tip:** When dealing with binomial distributions, always compare the result with two standard deviations from the mean to assess whether a value is significantly high or low.

A survey showed that 37% of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 27 human resource professionals are randomly selected, would 16 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?

This problem analyzes whether 16 HR professionals, out of a sample of 27, who reject candidates based on social media information is significantly high. It involves the binomial distribution with a 37% probability and explores key concepts such as mean, standard deviation, and significance.

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