Each month, Mechanical Engineering surveys its readers with an online “Question of the Month.” One issue reported on the responses to the question, “Do you feel you know enough about the latest computer-aided design (CAD) technologies to do your job?” The results: 44% answered “yes,” 12% answered “no, but I’m not worried about it,” 35% answered “no, and it concerns me,” and 9% answered “I don’t need to know CAD in my job.” Assume 1,000 readers responded to the online survey.

a. Find and interpret a 95% confidence interval for the proportion of readers who feel they know enough about CAD to do their job.

b. Find and interpret a 95% confidence interval for the difference between the proportions of readers who answered “no, but I’m not worried about it” and of those who answered “no, and it concerns me.”