Assume that when human resource managers are randomly​ selected, 

3838​% 

say job applicants should follow up within two weeks. If 

66 

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

22 

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

We are dealing with a binomial probability problem. The binomial distribution is used because we have a fixed number of trials (66 human resource managers), two possible outcomes for each trial (they either say job applicants should follow up within two weeks, or they don't), and a constant probability of success (38% or 0.38).

The probability of exactly 22 successes in 66 trials is given by the binomial probability formula:

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

Where:
- \(n = 66\) is the number of trials,
- \(k = 22\) is the number of successes,
- \(p = 0.38\) is the probability of success,
- \(1 - p = 0.62\) is the probability of failure.

Now, we can calculate this probability using the formula.

Let me calculate it.The probability that exactly 22 out of 66 human resource managers say that job applicants should follow up within two weeks is approximately 0.076, or 7.6%.

Would you like further details on the calculation, or have any other questions?

Here are five related questions to explore:
1. What is the probability that fewer than 22 managers say applicants should follow up within two weeks?
2. How would the probability change if the sample size was increased to 100 managers?
3. What is the expected number of managers who say applicants should follow up within two weeks?
4. How do you calculate cumulative probabilities in a binomial distribution?
5. How does the binomial distribution compare to a normal approximation for large sample sizes?

**Tip**: The binomial distribution becomes more symmetric as the sample size increases, especially when the probability of success is close to 0.5.

Assume that when human resource managers are randomly selected, 38% say job applicants should follow up within two weeks. If 66 human resource managers are randomly selected, find the probability that exactly 22 of them say job applicants should follow up within two weeks.

Find the probability that exactly 22 out of 66 human resource managers say job applicants should follow up within two weeks. This problem applies the binomial distribution formula with a success probability of 38%. Learn how to calculate exact binomial probabilities and explore related questions.

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