This problem can be solved using the binomial probability formula, which is used when there are only two outcomes: success or failure. In this case, success is defined as an HR manager saying that job applicants should follow up within two weeks, and failure is the opposite.

Step-by-Step Solution

Step 1: Define the parameters for the binomial distribution.

• The probability of success, $p = 0.57$ (57%).
• The probability of failure, $q = 1 - p = 0.43$.
• The number of trials (HR managers), $n = 6$.
• The minimum number of successes (at least 2 managers say follow up), $x \geq 2$.

Step 2: Use the complement rule to find the probability.

It’s easier to calculate the probability of fewer than 2 successes, and then subtract from 1 to find the probability of at least 2 successes:

$P(\text{at least 2 successes}) = 1 - P(\text{0 or 1 success})$

This means we need to find the probabilities for:

1. 0 successes
2. 1 success

Step 3: Use the binomial probability formula.

The binomial probability formula is:

$P(X = k) = \binom{n}{k} p^k q^{n-k}$

Where:

• $\binom{n}{k}$ is the binomial coefficient (combinations),
• $p$ is the probability of success,
• $q$ is the probability of failure,
• $n$ is the number of trials,
• $k$ is the number of successes.

Now calculate for:

1. $P(X = 0)$
2. $P(X = 1)$

Step 4: Calculate probabilities.

Let's calculate $P(X = 0)$ and $P(X = 1)$, then find $P(X \geq 2)$.

I'll compute these probabilities now.The probability that at least 2 of the 6 randomly selected human resource managers say job applicants should follow up within two weeks is 0.9434.

Would you like further details or have any other questions?

Here are 5 related questions to explore:

1. What is the probability that exactly 2 managers say follow up within two weeks?
2. How would the result change if the probability of success were different, say 70%?
3. What is the probability that none of the managers recommend following up?
4. How is the binomial distribution different from a normal distribution?
5. How can this method be applied to larger populations, like 100 HR managers?

Tip: The complement rule is often useful when it's easier to calculate the opposite scenario.