Final answer:
The probability that exactly three out of eight randomly selected human resource managers will say job applicants should follow up within two weeks is approximately 0.18 or 18%, which is calculated using the binomial probability formula.
Step-by-step explanation:
To find the probability that exactly 3 out of 8 randomly selected human resource managers say job applicants should follow up within two weeks, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability that exactly k managers say applicants should follow up within two weeks.
- C(n, k) is the number of combinations of n things taken k at a time.
- p is the probability of a manager saying applicants should follow up within two weeks (42% or 0.42).
- n is the total number of managers selected (8 in this case).
- k is the exact number of managers we're looking to find the probability for (3 in this case).
Using the given values, we compute:
C(8, 3) = 8! / (3! * (8 - 3)!) = 56
Therefore, P(X = 3) = 56 * (0.42)^3 * (1 - 0.42)^(8 - 3) = 56 * 0.074088 * 0.182520 = 0.754716
Hence, the probability that exactly 3 out of 8 human resource managers say job applicants should follow up within two weeks is approximately 0.18 or 18%.