Final answer:
To calculate the probability that at least 8 out of 10 human resource managers recommend following up within two weeks, we use the Binomial Probability Formula for P(X = 8), P(X = 9), and P(X = 10) and add the results.
Step-by-step explanation:
The question asks to find the probability that at least 8 out of 10 human resource managers say job applicants should follow up within two weeks, given that 59% say they should. To solve this, we use the Binomial Probability Formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- n = number of trials (human resource managers)
- k = number of successes (managers saying to follow up)
- p = probability of success on a single trial
- C(n, k) = combination of n items taken k at a time
To find the probability of 'at least 8,' we must consider P(X = 8), P(X = 9), and P(X = 10), then add these probabilities together. We have to compute each one separately:
For P(X = 8):
C(10, 8) * (0.59)^8 * (0.41)^2
For P(X = 9):
C(10, 9) * (0.59)^9 * (0.41)
For P(X = 10):
C(10, 10) * (0.59)^10
We sum these probabilities to get the overall probability of at least 8 managers agreeing.