American workers are increasingly planning to delay retirement (US News & World Report, June 30, 2010). According to a Pew Research Center comprehensive survey, 35% of employed adults of age 62 and older say they have pushed back their retirement date.

a. What is the probability that in a sample of 100 employed adults of age 62 and older, more than 40% have pushed back their retirement date?

b. What is the probability that in a sample of 200 employed adults of age 62 and older, more than 40% have pushed back their retirement date?

c. Comment on the difference between the two estimated probabilities.