The Employee Benefit Research Institute reports that 58% of workers say they are confident they have saved enough for retirement (source: “The 2015 Retirement Confidence Survey: Having a retirement savings plan a key factor in Americans’ retirement confidence, EBRI Issue Brief #413, April 2015).

a. If a random sample of 30 workers is taken, what is the probability that fewer than 17 workers are confident?

b. If a random sample of 50 workers is taken, what is the probability that more than 40 workers are confident about their retirement savings?