Meeting job requirements. Robert Half is a recruitment agency that connects employers and job seekers. According to a 2019 PR Newswire article, Robert Half said that on average human resource (HR) managers find that 42% of all resumes received are from candidates who do not meet the job requirements. Suppose an HR manager uses this data to determine the probability that the resumes she has received are from candidates who do not meet the job requirements. She has received 25 resumes.

a. What assumptions must be made and what information must be known to use the binomial probability distribution to calculate the probability that the resumes that the HR manager has received are from candidates who do not meet the job requirements?

b. Let x represent the number of received resumes that are from candidates who do not meet the job requirements, which can be adequately characterized by a binomial probability distribution. Find the mean and standard deviation of the binomial distribution.

c. Refer to part

b. If x has a binomial distribution, then so does the number, y, of resumes from candidates who do meet the job requirements. Describe the distribution of y. In particular, what are p, q, and n? Also, find E(y) and the standard deviation of y.