Assume that when human resource managers are randomly​ selected, 

4343​% 

say job applicants should follow up within two weeks. If 

55 

human resource managers are randomly​ selected, find the probability that exactly 

33 

of them say job applicants should follow up within two weeks.

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Part 1

The probability is 

enter your response here.

​(Round to four decimal places as​ needed.)

This problem can be modeled using a **binomial probability distribution** since we have a fixed number of trials (selecting 55 human resource managers), each with two outcomes (either the manager says applicants should follow up or they don't), and the probability of success (that the manager says they should follow up) is the same for each trial.

We can use the **binomial probability formula**:

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

Where:
- \( n = 55 \) is the number of trials (managers),
- \( k = 33 \) is the number of successes (managers who say applicants should follow up within two weeks),
- \( p = 0.4343 \) is the probability of success,
- \( 1 - p = 0.5657 \) is the probability of failure.

Now let's calculate the probability using this formula. I'll do the math.The probability that exactly 33 out of 55 human resource managers say job applicants should follow up within two weeks is approximately **0.0052** (rounded to four decimal places).

Would you like more details on this calculation or have any questions?

Here are 5 related questions to further explore the topic:
1. What is the probability that fewer than 30 managers say applicants should follow up?
2. How would the probability change if we increased the sample size to 100 managers?
3. What is the probability of 33 or more managers saying applicants should follow up?
4. How does the binomial distribution compare to the normal distribution for large samples?
5. Can the binomial distribution be approximated using a normal distribution for this problem?

**Tip**: For large \(n\), the binomial distribution can often be approximated by a normal distribution, making calculations simpler.

Assume that when human resource managers are randomly selected, 43.43% say job applicants should follow up within two weeks. If 55 human resource managers are randomly selected, find the probability that exactly 33 of them say job applicants should follow up within two weeks. (Round to four decimal places as needed.)

Learn how to calculate the probability that exactly 33 out of 55 human resource managers say job applicants should follow up within two weeks, using the binomial distribution formula. This problem highlights important concepts in probability and binomial distribution, making it ideal for students in Grades 10-12.

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