Solved:
Answered by AI, Verified by Human Experts
Assume that when human resource managers are randomly selected, 41% say job applicants should follow up within two weeks. If 8 human resource managers are randomly selected, find the probability that at least 4 of them say job applicants should follow up within two weeks.
Assume that when human resource managers are randomly selected, 41% say job applicants should follow up within two weeks. If 8 human resource managers are randomly selected, find the probability that at least 4 of them say job applicants should follow up within two weeks.
the probability that at least 4 out of 8 randomly selected human resource managers say job applicants should follow up within two weeks is approximately 0.7498.To solve this problem, we can use the binomial probability formula, which is given by:Where:-is the probability of getting exactly \( k \) successes,- ( n ) is the number of trials (in this case, the number of human resource managers selected),- ( k ) is the number of successes we're interested in (in this case, at least 4),- ( p ) is the probability of success in a single trial (in this case, the probability that a human resource manager says job applicants should follow up within two weeks).Given:-(8 human resource managers selected),-(probability that a human resource manager says job applicants should follow up within two weeks),-(at least 4 human resource managers saying job applicants should follow up within two weeks).To find the probability of at least 4 successes, we sum the probabilities of getting exactly 4, 5, 6, 7, or 8 successes.Let's calculate each term separately:We'll calculate each of these probabilities and then sum them up to findLet's calculate each term:Now, let's calculateusing similar calculations.Now, let's sum these probabilities:So, the probability that at least 4 out of 8 randomly selected human resource managers say job applicants should follow up within two weeks is approximately 0.7498....