Final answer:
The question is about calculating the probability of exactly 13 out of 20 human resource managers saying job applicants should follow up within two weeks. This can be done using the binomial probability formula which takes into account the number of managers, the fixed probability, and the number of successes among the managers questioned.
Step-by-step explanation:
The subject of the question is to calculate the probability that exactly 13 out of 20 human resource managers will say job applicants should follow up within two weeks. This is a binomial probability problem since there are two possible outcomes for each manager (either they say applicants should follow up within two weeks or they don't), there is a fixed number of trials (20 managers), each trial is independent, and the probability of success (managers saying applicants should follow up within two weeks) remains constant at 53% or 0.53.
To calculate the probability of exactly 13 out of 20 managers saying applicants should follow up, we use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
X is the random variable representing the number of successesk is the number of successes we're looking for (in this case, 13),n is the number of trials (20 managers),p is the probability of success on any given trial (0.53),and (n choose k) is the number of combinations of n things taken k at a time.
Substituting the given values we have:
P(X = 13) = (20 choose 13) * (0.53)^13 * (0.47)^7
The number of ways to choose 13 managers out of 20 can be calculated using the combination formula, or looked up in a binomial coefficient table. Then, the resulting value is multiplied with the respective probabilities raised to the power of the number of successes and failures, respectively.
Calculating these gives us the probability of exactly 13 managers saying applicants should follow up within two weeks.