Question

Assume that when human resource managers are randomly​ selected, 59​% say job applicants should follow up within two weeks. if 10 human resource managers are randomly​ selected, find the probability that at least 8 of them say job applicants should follow up within two weeks.

Answer 1

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.