Final answer:
The college-level question in mathematics asks for the probability that at least 14 out of 20 human resource managers would recommend that job applicants follow up within two weeks, given that there is a 63% chance of any one of them recommending it. The calculation uses the binomial distribution formula and would be typically accomplished with statistical software or a probability table.
Step-by-step explanation:
The subject of this question involves calculating the probability of a certain number of successes in a binomial distribution, which falls under the subject of Mathematics, specifically probability and statistics, at the College level.
To find the probability that at least 14 of 20 human resource managers say job applicants should follow up within two weeks, when 63% of them agree to this statement, we use the binomial probability formula:
P(X ≥ k) = 1 - P(X < k)
where X is the number of successes (managers who say applicants should follow up), k is the specific number of successes we're interested in, and P is the probability. As this calculation involves numerous steps, it is often done using statistical software or a binomial probability table.
In this case, we need the cumulative probability of getting 13 or fewer successes, and then subtracting that value from 1 to get the probability of at least 14 successes:
P(X ≥ 14) = 1 - P(X ≤ 13).
Considering we are dealing with a binomial distribution, each trial is independent, and the probability of success remains constant at 63% for each human resource manager selected.